Matematická konstanta je číslo, které má pro výpočty zvláštní význam. Například konstanta π (vyslovuje se "koláč") znamená poměr obvodu kruhu k jeho průměru. Tato hodnota je vždy stejná pro jakoukoli kružnici. Matematická konstanta je často reálné, neintegrální číslo, které nás zajímá.
Na rozdíl od fyzikálních konstant nepocházejí matematické konstanty z fyzikálních měření.
Následující tabulka obsahuje některé důležité matematické konstanty:
| Název | Symbol | Hodnota | Význam |
| Pí, Archimédova konstanta nebo Ludophovo číslo | π | ≈3.141592653589793 | Transcendentní číslo, které je poměrem délky obvodu kruhu k jeho průměru. Je to také plocha jednotkového kruhu. |
| E, Napierova konstanta | e | ≈2.718281828459045 | Transcendentní číslo, které je základem přirozených logaritmů, někdy nazývané "přirozené číslo". |
| φ | 5 + 1 2 ≈ 1,618 {\displaystyle {\frac {{\sqrt {5}}+1}{2}}\aprox 1,618} | Je to hodnota větší hodnoty dělená menší hodnotou, pokud se rovná hodnotě součtu hodnot dělené větší hodnotou. | |
| Druhá odmocnina ze 2, Pythagorova konstanta | 2 {\displaystyle {\sqrt {2}}} | ≈ 1.414 {\displaystyle \aprox 1.414} | Iracionální číslo, které je délkou úhlopříčky čtverce o délce strany 1. Toto číslo nelze zapsat jako zlomek. |
Následující tabulka obsahuje seznam konstant a řad v matematice s následujícími sloupci:
Všimněte si, že seznam lze odpovídajícím způsobem seřadit kliknutím na záhlaví v horní části tabulky.
| Hodnota | Název | Symbol | LaTeX | Vzorec | Typ | OEIS | Pokračující frakce |
| 3.24697960371746706105000976800847962 | Stříbro, Tutte-Beraha konstantní | ς {\displaystyle \varsigma } | 2 + 2 cos ( 2 π / 7 ) = 2 + 2 + 7 + 7 7 + 7 7 + ⋯ 3 3 3 1 + 7 + 7 7 + 7 7 + ⋯ 3 3 3 {\displaystyle 2+2\cos(2\pi /7)=\textstyle 2+{\frac {2+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}{1+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}}} | 2+2 cos(2Pi/7) | T | A116425 | [3;4,20,2,3,1,6,10,5,2,2,1,2,2,1,18,1,1,3,2,...] |
| 1.09864196439415648573466891734359621 | Pařížská konstanta | C P a {\displaystyle C_{Pa}} | ∏ n = 2 ∞ 2 φ φ + φ n , φ = F i {\displaystyle \prod _{n=2}^{\infty }{\frac {2\varphi }{\varphi +\varphi _{n}}}\;,\varphi ={Fi}}. | I | A105415 | [1;10,7,3,1,3,1,5,1,4,2,7,1,2,3,22,1,2,5,2,1,...] | |
| 2.74723827493230433305746518613420282 | Ramanujanův vnořený radikál R 5 | R 5 {\displaystyle R_{5}} | 5 + 5 + 5 - 5 + 5 + 5 + 5 - ⋯ = 2 + 5 + 15 - 6 5 2 {\displaystyle \scriptstyle {\sqrt {5+{\sqrt {5+{\sqrt {5-{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5-\cdots }}}}}}}}}}}}}}\;=\textstyle {\frac {2+{\sqrt {5}}+{\sqrt {15-6{\sqrt {5}}}}}{2}}}. | (2+sqrt(5)+sqrt(15-6 sqrt(5)))/2 | I | [2;1,2,1,21,1,7,2,1,1,2,1,2,1,17,4,4,1,1,4,2,...] | |
| 2.23606797749978969640917366873127624 | Druhá odmocnina z 5, Gaussův součet | 5 {\displaystyle {\sqrt {5}}} | ∀ n = 5 , ∑ k = 0 n - 1 e 2 k 2 π i n = 1 + e 2 π i 5 + e 8 π i 5 + e 18 π i 5 + e 32 π i 5 {\displaystyle \scriptstyle \forall \,n=5,\displaystyle \sum _{k=0}^{n-1}e^{\frac {2k^{2}\pi i}{n}}=1+e^{\frac {2\pi i}{5}}+e^{\frac {8\pi i}{5}}+e^{\frac {18\pi i}{5}}+e^{\frac {32\pi i}{5}}}. | Součet[k=0 až 4]{e^(2k^2 pi i/5)} | I | A002163 | [2;4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,...] |
| 3.62560990822190831193068515586767200 | Gama(1/4) | Γ ( 1 4 ) {\displaystyle \Gamma ({\tfrac {1}{4}})} | 4 ( 1 4 ) ! = ( - 3 4 ) ! {\displaystyle 4\left({\frac {1}{4}}}\right)!=\left(-{\frac {3}{4}}}\right)! } | 4(1/4)! | T | A068466 | [3;1,1,1,2,25,4,9,1,1,8,4,1,6,1,1,19,1,1,4,1,...] |
| 0.18785964246206712024851793405427323 | MRB constant, Marvin Ray Burns | C M R B {\displaystyle C_{_{MRB}}} | ∑ n = 1 ∞ ( - 1 ) n ( n 1 / n - 1 ) = - 1 1 + 2 2 - 3 3 + 4 4 ... {\displaystyle \sum _{n=1}^{\infty }({-}1)^{n}(n^{1/n}{-}1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+{\sqrt[{4}]{4}}},\dots } | Součet[n=1 až ∞]{(-1)^n (n^(1/n)-1)} | T | A037077 | [0;5,3,10,1,1,4,1,1,1,1,9,1,1,12,2,17,2,2,1,...] |
| 0.11494204485329620070104015746959874 | Keplerova-Bouwkampova konstanta | ρ {\displaystyle {\rho }} | ∏ n = 3 ∞ cos ( π n ) = cos ( π 3 ) cos ( π 4 ) cos ( π 5 ) ... {\displaystyle \prod _{n=3}^{\infty }\cos \left({\frac {\pi }{n}}}\right)=\cos \left({\frac {\pi }{3}}\right)\cos \left({\frac {\pi }{4}}\right)\cos \left({\frac {\pi }{5}}\right)\dots } | prod[n=3 až ∞]{cos(pi/n)} | T | A085365 | [0;8,1,2,2,1,272,2,1,41,6,1,3,1,1,26,4,1,1,...] |
| 1.78107241799019798523650410310717954 | Exp(gamma) | e γ {\displaystyle e^{\gamma }} | ∏ n = 1 ∞ e 1 n 1 + 1 n = ∏ n = 0 ∞ ( ∏ k = 0 n ( k + 1 ) ( - 1 ) k + 1 ( n k ) ) 1 n + 1 = {\displaystyle \prod _{n=1}^{\infty }{\frac {e^{\frac {1}{n}}}{1+{\tfrac {1}{n}}}}=\prod _{n=0}^{\infty }\left(\prod _{k=0}^{n}(k+1)^{(-1)^{k+1}{n \choose k}}}\right)^{\frac {1}{n+1}}=} ( 2 1 ) 1 / 2 ( 2 2 1 ⋅ 3 ) 1 / 3 ( 2 3 ⋅ 4 1 ⋅ 3 3 ) 1 / 4 ( 2 4 ⋅ 4 4 1 ⋅ 3 6 ⋅ 5 ) 1 / 5 ... {\displaystyle \textstyle \left({\frac {2}{1}}}\right)^{1/2}\left({\frac {2^{2}}{1\cdot 3}}}\right)^{1/3}\left({\frac {2^{3}\cdot 4}{1\cdot 3^{3}}}pravá)^{1/4}\levá({\frac {2^{4}\cdot 4^{4}}{1\cdot 3^{6}\cdot 5}}}pravá)^{1/5}\dots } | Prod[n=1 až ∞]{e^(1/n)}/{1 + 1/n} | T | A073004 | [1;1,3,1,1,3,5,4,1,1,2,2,1,7,9,1,16,1,1,1,2,...] |
| 1.28242712910062263687534256886979172 | Glaisher-Kinkelinova konstanta | A {\displaystyle {A}} | e 1 12 - ζ ′ ( - 1 ) = e 1 8 - 1 2 ∑ n = 0 ∞ 1 n + 1 ∑ k = 0 n ( - 1 ) k ( n k ) ( k + 1 ) 2 ln ( k + 1 ) {\displaystyle e^{{\frac {1}{12}}-\zeta ^{\prime }(-)1)}=e^{{\frac {1}{8}}-{\frac {1}{2}}\součet \limits _{n=0}^{\infty }{\frac {1}{n+1}}\součet \limits _{k=0}^{n}\left(-1\right)^{k}{\binom {n}{k}}\left(k+1\right)^{2}\ln(k+1)}}} | e^(1/2-zeta´{-1}) | T | A074962 | [1;3,1,1,5,1,1,1,3,12,4,1,271,1,1,2,7,1,35,...] |
| 7.38905609893065022723042746057500781 | Schwarzschildova kuželová konstanta | e 2 {\displaystyle e^{2}} | ∑ n = 0 ∞ 2 n n ! = 1 + 2 + 2 2 2 ! + 2 3 3 ! + 2 4 4 ! + 2 5 5 ! + ... {\displaystyle \sum _{n=0}^{\infty }{\frac {2^{n}}{n!}}=1+2+{\frac {2^{2}}{2!}}+{\frac {2^{3}}{3!}}+{\frac {2^{4}}{4!}}+{\frac {2^{5}}{5!}}+\dots } | Součet[n=0 až ∞]{2^n/n!} | T | A072334 | [7;2,1,1,3,18,5,1,1,6,30,8,1,1,9,42,11,1,...] |
| 1.01494160640965362502120255427452028 | Gieseking konstanta | G G i {\displaystyle {G_{Gi}}} | 3 3 4 ( 1 - ∑ n = 0 ∞ 1 ( 3 n + 2 ) 2 + ∑ n = 1 ∞ 1 ( 3 n + 1 ) 2 ) = {\displaystyle {\frac {3{\sqrt {3}}}{4}}\left(1-\součet _{n=0}^{\infty }{\frac {1}{(3n+2)^{2}}}+\součet _{n=1}^{\infty }{\frac {1}{(3n+1)^{2}}}}\pravo)=} 3 3 4 ( 1 - 1 2 2 + 1 4 2 - 1 5 2 + 1 7 2 - 1 8 2 + 1 10 2 ± ... ) {\displaystyle \textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \dots \right)} | T | A143298 | [1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...] | |
| 2.62205755429211981046483958989111941 | Lemniscata konstantní | ϖ {\displaystyle {\varpi }} | π G = 4 2 π ( 1 4 ! ) 2 {\displaystyle \pi \,{G}=4{\sqrt {\tfrac {2}{\pi }}},({\tfrac {1}{4}}}!)^{2}}} | 4 sqrt(2/pi) (1/4!)^2 | T | A062539 | [2;1,1,1,1,1,4,1,2,5,1,1,1,14,9,2,6,2,9,4,1,...] |
| 0.83462684167407318628142973279904680 | Gaussova konstanta | G {\displaystyle {G}} | 1 a g m ( 1 , 2 ) = 4 2 ( 1 4 ! ) 2 π 3 / 2 A g m : A r i t h m e t i c - g e o m e t r i c k ý m e n {\displaystyle {\underset {Agm:\;Aritmeticko-geometrický\;mean}{{\frac {1}{\mathrm {agm} (1,{\sqrt {2}})}}={\frac {4{\sqrt {2}},({\tfrac {1}{4}}!)^{2}}{\pi ^{3/2}}}}}} | (4 sqrt(2)(1/4!)^2)/pi^(3/2) | T | A014549 | [0;1,5,21,3,4,14,1,1,1,1,1,3,1,15,1,3,7,1,...] |
| 1.01734306198444913971451792979092052 | Zeta(6) | ζ ( 6 ) {\displaystyle \zeta (6)} | π 6 945 = ∏ n = 1 ∞ 1 1 - p n - 6 p n : p r i m o = 1 1 - 2 - 6 ⋅ 1 1 - 3 - 6 ⋅ 1 1 - 5 - 6 . . . {\displaystyle {\frac {\pi ^{6}}{945}}=\prod _{n=1}^{\infty }{\underset {p_{n}:\,{primo}}{\frac {1}{{1-p_{n}}^{-6}}}}={\frac {1}{1{-}2^{-6}}}{\cdot }{\frac {1}{1{-}3^{-6}}}{\cdot }{\frac {1}{1{-}5^{-6}}}... } | Prod[n=1 až ∞] {1/(1-ithprime(n)^-6)} | T | A013664 | [1;57,1,1,1,15,1,6,3,61,1,5,3,1,6,1,3,3,6,1,...] |
| 0,60792710185402662866327677925836583 | Constante de Hafner-Sarnak-McCurley | 1 ζ ( 2 ) {\displaystyle {\frac {1}{\zeta (2)}}} | 6 π 2 = ∏ n = 0 ∞ ( 1 - 1 p n 2 ) p n : p r i m o = ( 1 - 1 2 2 ) ( 1 - 1 3 2 ) ( 1 - 1 5 2 ) ... {\displaystyle {\frac {6}{\pi ^{2}}}{=}\prod _{n=0}^{\infty }{\underset {p_{n}:\,{primo}}{\left(1-{\frac {1}{{p_{n}}^{2}}}}\right)}}{=}\textstyle \left(1{-}{\frac {1}{2^{2}}}}\right)\left(1{-}{\frac {1}{3^{2}}}}\right)\left(1{-}{\frac {1}{5^{2}}}}\right)\dots } | Prod{n=1 až ∞} (1-1/ithprime(n)^2) | T | A059956 | [0;1,1,1,1,4,2,4,7,1,4,2,3,4,10,1,2,1,1,1,...] |
| 1.11072073453959156175397024751517342 | Poměr čtverce a kružnice vepsané nebo vepsané do kružnice | π 2 2 {\displaystyle {\frac {\pi }{2{\sqrt {2}}}}} | ∑ n = 1 ∞ ( - 1 ) ⌊ n - 1 2 ⌋ 2 n + 1 = 1 1 + 1 3 - 1 5 - 1 7 + 1 9 + 1 11 - ... {\displaystyle \sum _{n=1}^{\infty }{\frac {(-1)^{\lfloor {\frac {n-1}{2}}}\rfloor }}{2n+1}}={\frac {1}{1}}+{\frac {1}{3}}-{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}+{\frac {1}{11}}-\dots } | sum[n=1 až ∞]{(-1)^(floor((n-1)/2))/(2n-1)} | T | A093954 | [1;9,31,1,1,17,2,3,3,2,3,1,1,2,2,1,4,9,1,3,...] |
| 2.80777024202851936522150118655777293 | Fransén-Robinson konstanta | F {\displaystyle {F}} | ∫ 0 ∞ 1 Γ ( x ) d x . = e + ∫ 0 ∞ e - x π 2 + ln 2 x d x {\displaystyle \int _{0}^{\infty }{\frac {1}{\Gamma (x)}}\,dx.=e+\int _{0}^{\infty }{\frac {e^{-x}}{\pi ^{2}+\ln ^{2}x}}\,dx} | N[int[0 až ∞] {1/Gamma(x)}] | T | A058655 | [2;1,4,4,1,18,5,1,3,4,1,5,3,6,1,1,1,5,1,1,1...] |
| 1.64872127070012814684865078781416357 | Odmocnina z čísla e | e {\displaystyle {\sqrt {e}}} | ∑ n = 0 ∞ 1 2 n n ! = ∑ n = 0 ∞ 1 ( 2 n ) ! ! = 1 1 + 1 2 + 1 8 + 1 48 + ⋯ {\displaystyle \sum _{n=0}^{\infty }{\frac {1}{2^{n}n!}}=\sum _{n=0}^{\infty }{\frac {1}{(2n)!!}}={\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{8}}+{\frac {1}{48}}+\cdots } | sum[n=0 až ∞]{1/(2^n n!)} | T | A019774 | [1;1,1,1,5,1,1,9,1,1,13,1,1,17,1,1,21,1,1,...] |
| i | Imaginární číslo | i {\displaystyle {i}} | - 1 = ln ( - 1 ) π e i π = - 1 {\displaystyle {\sqrt {-1}}={\frac {\ln(-1)}{\pi }}\qquad \qquad \mathrm {e} ^{i\,\pi }=-1} | sqrt(-1) | C | ||
| 262537412640768743.999999999999250073 | Hermitova-Ramanujanova konstanta | R {\displaystyle {R}} | e π 163 {\displaystyle e^{\pi {\sqrt {163}}}} | e^(π sqrt(163)) | T | A060295 | [262537412640768743;1,1333462407511,1,8,1,1,5,...] |
| 4.81047738096535165547303566670383313 | John constant | γ {\displaystyle \gamma } | i i = i - i = i 1 i = ( i i ) - 1 = e π 2 {\displaystyle {\sqrt[{i}]{i}}=i^{-i}=i^{\frac {1}{i}}=(i^{i})^{-1}=e^{\frac {\pi }{2}}}} | e^(π/2) | T | A042972 | [4;1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,3,...] |
| 4.53236014182719380962768294571666681 | Constante de Van der Pauw | α {\displaystyle \alpha } | π l n ( 2 ) = ∑ n = 0 ∞ 4 ( - 1 ) n 2 n + 1 ∑ n = 1 ∞ ( - 1 ) n + 1 n = 4 1 - 4 3 + 4 5 - 4 7 + 4 9 - ... 1 1 - 1 2 + 1 3 - 1 4 + 1 5 - ... {\displaystyle {\frac {\pi }{ln(2)}}={\frac {\součet _{n=0}^{\infty }{\frac {4(-1)^{n}}{2n+1}}}{\součet _{n=1}^{{\infty }{\frac {(-1)^{n+1}}{n}}}}={\frac {{\frac {4}{1}}{-}{\frac {4}{3}}{+}{\frac {4}{5}}{-}{\frac {4}{7}}{+}{\frac {4}{9}}-\bodů }{{\frac {1}{1}}{-}{\frac {1}{2}}{+}{\frac {1}{3}}{-}{\frac {1}{4}}{+}{\frac {1}{5}}-\bodů }}}. | π/ln(2) | T | A163973 | [4;1,1,7,4,2,3,3,1,4,1,1,4,7,2,3,3,12,2,1,...] |
| 0.76159415595576488811945828260479359 | Hyperbolický tangens (1) | t h 1 {\displaystyle th\,1} | e - 1 e e + 1 e = e 2 - 1 e 2 + 1 {\displaystyle {\frac {e-{\frac {1}{e}}}{e+{{\frac {1}{e}}}}={\frac {e^{2}-1}{e^{2}+1}}}) | (e-1/e)/(e+1/e) | T | A073744 | [0;1,3,5,7,9,11,13,15,17,19,21,23,25,27,...] |
| 0.69777465796400798200679059255175260 | Konstanta pokračující frakce | C C F {\displaystyle {C}_{CF}} | J 1 ( 2 ) J 0 ( 2 ) F u n k c e J k ( ) B e s e l = ∑ n = 0 ∞ n n ! n ! ∑ n = 0 ∞ 1 n ! n ! = 0 1 + 1 1 + 2 4 + 3 36 + 4 576 + ... 1 1 + 1 1 + 1 4 + 1 36 + 1 576 + ... {\displaystyle {\underset {J_{k}(){Bessel}}{\underset {Funkce}{\frac {J_{1}(2)}{J_{0}(2)}}}}={\frac {\sum \limits _{n=0}^{\infty }{\frac {n}{n!n!}}}{\sum \limits _{n=0}^{\infty }{\frac {1}{n!n!}}}}={{\frac {{\frac {0}{1}}+{\frac {1}{1}}+{\frac {2}{4}}+{\frac {3}{36}}+{\frac {4}{576}}+{\dots }{{\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{4}}+{\frac {1}{36}}+{\frac {1}{576}}}+{\dots }}}} | (součet {n=0 až inf} n/(n!n!)) /(součet {n=0 až inf} 1/(n!n!)) | A052119 | [0;1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,...] | |
| 0.36787944117144232159552377016146086 | Inverzní Napierova konstanta | 1 e {\displaystyle {\frac {1}{e}}} | ∑ n = 0 ∞ ( - 1 ) n n ! = 1 0 ! - 1 1 ! + 1 2 ! - 1 3 ! + 1 4 ! - 1 5 ! + ... {\displaystyle \sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!}}={\frac {1}{0!}}-{\frac {1}{1!}}+{\frac {1}{2!}}-{\frac {1}{3!}}+{\frac {1}{4!}}-{\frac {1}{5!}}+\dots } | sum[n=2 až ∞]{(-1)^n/n!} | T | A068985 | [0;2,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,...] |
| 2.71828182845904523536028747135266250 | Napierova konstanta | e {\displaystyle e} | ∑ n = 0 ∞ 1 n ! = 1 0 ! + 1 1 + 1 2 ! + 1 3 ! + 1 4 ! + 1 5 ! + ⋯ {\displaystyle \sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1}}+{\frac {1}{2!}}+{\frac {1}{3!}}+{\frac {1}{4!}}+{\frac {1}{5!}}+\cdots } | Součet[n=0 až ∞]{1/n!} | T | A001113 | [2;1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...] |
| 0.49801566811835604271369111746219809 | Faktoriál i | i ! {\displaystyle i\,! } | Γ ( 1 + i ) = i Γ ( i ) {\displaystyle \Gamma (1+i)=i\,\Gamma (i)} | Gamma(1+i) | C | A212877 | [0;6,2,4,1,8,1,46,2,2,3,5,1,10,7,5,1,7,2,...] |
| 0.43828293672703211162697516355126482 | Nekonečný | ∞ i {\displaystyle {}^{\infty }i} | lim n → ∞ n i = lim n → ∞ i ⋅ ⋅ i ⏟ n {\displaystyle \lim _{n\to \infty }{}^{n}i=\lim _{n\to \infty }\podtrženo {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}} | i^i^i^... | C | A077589 | [0;2,3,1,1,4,2,2,1,10,2,1,3,1,8,2,1,2,1, ...] |
| 0.56755516330695782538461314419245334 | Modul | | ∞ i | {\displaystyle |{}^{\infty }i|} | lim n → ∞ | n i | = | lim n → ∞ i i ⋅ ⋅ i ⏟ n | {\displaystyle \lim _{n\to \infty }\left|{}^{n}i\right|=\left|\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}\vpravo|} | Mod(i^i^i^...) | A212479 | [0;1,1,3,4,1,58,12,1,51,1,4,12,1,1,2,2,3,...] | |
| 0.26149721284764278375542683860869585 | Meissel-Mertensova konstanta | M {\displaystyle M} | lim n → ∞ ( ∑ p ≤ n 1 p - ln ( ln ( n ) ) ) {\displaystyle \lim _{n\rightarrow \infty }\left(\sum _{p\leq n}{\frac {1}{p}}-\ln(\ln(n))\right)} | A077761 | [0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,...] | ||
| 1.9287800... | Wrightova konstanta | ω {\displaystyle \omega } | ⌊ 2 2 2 ⋅ ⋅ 2 ω ⌋ {\displaystyle \left\lfloor 2^{2^{2^{\cdot ^{\cdot ^{2^{\omega }}}}}}\right\rfloor } | A086238 | [1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3] | ||
| 0.37395581361920228805472805434641641 | Artin konstantní | C A r t i n {\displaystyle C_{Artin}} | ∏ n = 1 ∞ ( 1 - 1 p n ( p n - 1 ) ) {\displaystyle \prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}(p_{n}-1)}}\right)} | T | A005596 | [0;2,1,2,14,1,1,2,3,5,1,3,1,5,1,1,2,3,5,46,...] | |
| 4.66920160910299067185320382046620161 | Feigenbaumova konstanta δ | δ {\displaystyle {\delta }} | lim n → ∞ x n + 1 - x n x n + 2 - x n + 1 x ∈ ( 3 , 8284 ; 3 , 8495 ) {\displaystyle \lim _{n\to \infty }{\frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}}\qquad \scriptstyle x\in (3,8284;\,3,8495)} x n + 1 = a x n ( 1 - x n ) o x n + 1 = a sin ( x n ) {\displaystyle \scriptstyle x_{n+1}=\,ax_{n}(1-x_{n})\quad {o}\quad x_{n+1}=\,a\sin(x_{n})} | T | A006890 | [4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,...] | |
| 2.50290787509589282228390287321821578 | Feigenbaumova konstanta α | α {\displaystyle \alpha } | lim n → ∞ d n d n + 1 {\displaystyle \lim _{n\to \infty }{\frac {d_{n}}{d_{n+1}}}} | T | A006891 | [2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,...] | |
| 5.97798681217834912266905331933922774 | Šestihranná konstanta Madelung 2 | H 2 ( 2 ) {\displaystyle H_{2}(2)} | π ln ( 3 ) 3 {\displaystyle \pi \ln(3){\sqrt {3}}} | Pi Log[3]Sqrt[3] | T | A086055 | [5;1,44,2,2,1,15,1,1,12,1,65,11,1,3,1,1,...] |
| 0.96894614625936938048363484584691860 | Beta(3) | β ( 3 ) {\displaystyle \beta (3)} | π 3 32 = ∑ n = 1 ∞ - 1 n + 1 ( - 1 + 2 n ) 3 = 1 1 3 - 1 3 3 + 1 5 3 - 1 7 3 + ... {\displaystyle {\frac {\pi ^{3}}{32}}=\sum _{n=1}^{\infty }{\frac {-1^{n+1}}{(-1+2n)^{3}}}={\frac {1}{1^{3}}}{-}{\frac {1}{3^{3}}}{+}{\frac {1}{5^{3}}}{-}{\frac {1}{7^{3}}}{+}\dots } | Součet[n=1 až ∞]{(-1)^(n+1)/(-1+2n)^3} | T | A153071 | [0;1,31,4,1,18,21,1,1,2,1,2,1,3,6,3,28,1,...] |
| 1.902160583104 | Brunova konstanta2 = Σ inverzní dvojčata | B 2 {\displaystyle B_{\,2}} | ∑ ( 1 p + 1 p + 2 ) p , p + 2 : p r i m o s = ( 1 3 + 1 5 ) + ( 1 5 + 1 7 ) + ( 1 11 + 1 13 ) + ... {\displaystyle \textstyle \sum {\underset {p,\,p+2:\,{primos}}{({\frac {1}{p}}+{\frac {1}{p+2}})}}=({\frac {1}{3}}{+}{\frac {1}{5}})+({\tfrac {1}{5}}{+}{\tfrac {1}{7}})+({\tfrac {1}{11}}{+}{\tfrac {1}{13}})+\dots } | A065421 | [1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2] | ||
| 0.870588379975 | Brunova konstanta4 = Σ inverzní číslo dvojčete. | B 4 {\displaystyle B_{\,4}} | ( 1 5 + 1 7 + 1 11 + 1 13 ) p , p + 2 , p + 4 , p + 6 : p r i m e s + ( 1 11 + 1 13 + 1 17 + 1 19 ) + ... {\displaystyle {\underset {p,\,p+2,\,p+4,\,p+6:\,{primes}}{\left({\tfrac {1}{5}}+{\tfrac {1}{7}}+{\tfrac {1}{11}}+{\tfrac {1}{13}}\right)}}+\left({\tfrac {1}{11}}+{\tfrac {1}{13}}+{\tfrac {1}{17}}+{\tfrac {1}{19}}\right)+\dots } | A213007 | [0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1] | ||
| 22.4591577183610454734271522045437350 | pi^e | π e {\displaystyle \pi ^{e}} | π e {\displaystyle \pi ^{e}} | pi^e | A059850 | [22;2,5,1,1,1,1,1,3,2,1,1,3,9,15,25,1,1,5,...] | |
| 3.14159265358979323846264338327950288 | Pí, Archimédova konstanta | π {\displaystyle \pi } | lim n → ∞ 2 n 2 - 2 + 2 + ⋯ + 2 ⏟ n {\displaystyle \lim _{n\to \infty }\,2^{n}\podle {\sqrt {2-{\sqrt {2+{\sqrt {2+\dots +{\sqrt {2}}}}}}}} _{n}} | Součet[n=0 až ∞]{(-1)^n 4/(2n+1)} | T | A000796 | [3;7,15,1,292,1,1,1,2,1,3,1,14,...] |
| 0.06598803584531253707679018759684642 | e - e {\displaystyle e^{-e}} | e - e {\displaystyle e^{-e}} | T | A073230 | [0;15,6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,...] | ||
| 0.20787957635076190854695561983497877 | i^i | i i {\displaystyle i^{i}} | e - π 2 {\displaystyle e^{\frac {-\pi }{2}}} | e^(-pi/2) | T | A049006 | [0;4,1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,...] |
| 0.28016949902386913303643649123067200 | Bernsteinova konstanta | β {\displaystyle \beta } | 1 2 π {\displaystyle {\frac {1}{2{\sqrt {\pi }}}}} | T | A073001 | [0;3,1,1,3,9,6,3,1,3,13,1,16,3,3,4,…] | |
| 0.28878809508660242127889972192923078 | Flajolet a Richmond | Q {\displaystyle Q} | ∏ n = 1 ∞ ( 1 - 1 2 n ) = ( 1 - 1 2 1 ) ( 1 - 1 2 2 ) ( 1 - 1 2 3 ) ... {\displaystyle \prod _{n=1}^{\infty }\levá(1-{\frac {1}{2^{n}}}}pravá)=\levá(1{-}{\frac {1}{2^{1}}}}pravá)\levá(1{-}{\frac {1}{2^{2}}}}pravá)\levá(1{-}{\frac {1}{2^{3}}}}pravá)\dots } | prod[n=1 až ∞]{1-1/2^n} | A048651 | ||
| 0.31830988618379067153776752674502872 | Inverzní hodnota čísla pí, Ramanujan | 1 π {\displaystyle {\frac {1}{\pi }}} | 2 2 9801 ∑ n = 0 ∞ ( 4 n ) ! ( 1103 + 26390 n ) ( n ! ) 4 396 4 n {\displaystyle {\frac {2{\sqrt {2}}}{9801}}\sum _{n=0}^{\infty }{\frac {(4n)!(1103+26390n)}{(n!)^{4}396^{4n}}}} | T | A049541 | [0;3,7,15,292,1,1,1,2,1,3,1,14,2,1,1,...] | |
| 0.47494937998792065033250463632798297 | Weierstraß konstanta | W W E {\displaystyle W_{_{WE}}} | e π 8 π 4 ∗ 2 3 / 4 ( 1 4 ! ) 2 {\displaystyle {\frac {e^{\frac {\pi }{8}}{\sqrt {\pi }}}{4*2^{3/4}{({\frac {1}{4}}!)^{2}}}}} | (E^(Pi/8) Sqrt[Pi])/(4 2^(3/4) (1/4)!^2) | T | A094692 | [0;2,9,2,11,1,6,1,4,6,3,19,9,217,1,2,...] |
| 0.56714329040978387299996866221035555 | Konstanta Omega | Ω {\displaystyle \Omega } | W ( 1 ) = ∑ n = 1 ∞ ( - n ) n - 1 n ! = 1 - 1 + 3 2 - 8 3 + 125 24 - ... {\displaystyle W(1)=\sum _{n=1}^{\infty }{\frac {(-n)^{n-1}}{n!}}=1{-}1{+}{\frac {3}{2}}{-}{\frac {8}{3}}{+}{\frac {125}{24}}-\dots } | sum[n=1 až ∞]{(-n)^(n-1)/n!} | T | A030178 | [0;1,1,3,4,2,10,4,1,1,1,1,2,7,306,1,5,1,...] |
| 0.57721566490153286060651209008240243 | Eulerovo číslo | γ {\displaystyle \gamma } | - ψ ( 1 ) = ∑ n = 1 ∞ ∑ k = 0 ∞ ( - 1 ) k 2 n + k {\displaystyle -\psi (1)=\sum _{n=1}^{\infty }\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{n}+k}}}. | sum[n=1 až ∞]|sum[k=0 až ∞]{((-1)^k)/(2^n+k)} | ? | A001620 | [0;1,1,2,1,2,1,4,3,13,5,1,1,8,1,2,...] |
| 0.60459978807807261686469275254738524 | Dirichletova řada | π 3 3 {\displaystyle {\frac {\pi }{3{\sqrt {3}}}}} | ∑ n = 1 ∞ 1 n ( 2 n n ) = 1 - 1 2 + 1 4 - 1 5 + 1 7 - 1 8 + ⋯ {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n{2n \choose n}}}=1-{\frac {1}{2}}+{\frac {1}{4}}-{\frac {1}{5}}+{\frac {1}{7}}-{\frac {1}{8}}+\cdots } | Součet[1/(n Binom[2 n, n]), {n, 1, ∞}] | T | A073010 | [0;1,1,1,1,8,10,2,2,3,3,1,9,2,5,4,1,27,27,...] |
| 0.63661977236758134307553505349005745 | 2/Pi, François Viète | 2 π {\displaystyle {\frac {2}{\pi }}} | 2 2 ⋅ 2 + 2 2 ⋅ 2 + 2 + 2 2 ⋯ {\displaystyle {\frac {\sqrt {2}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2}}}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}{2}}\cdots } | T | A060294 | [0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...] | |
| 0.66016181584686957392781211001455577 | Dvojitá primární konstanta | C 2 {\displaystyle C_{2}} | ∏ p = 3 ∞ p ( p - 2 ) ( p - 1 ) 2 {\displaystyle \prod _{p=3}^{\infty }{\frac {p(p-2)}{(p-1)^{2}}}} | prod[p=3 až ∞]{p(p-2)/(p-1)^2 | A005597 | [0;1,1,1,16,2,2,2,2,1,18,2,2,11,1,1,2,4,1,...] | |
| 0.66274341934918158097474209710925290 | Laplaceova limitní konstanta | λ {\displaystyle \lambda } | A033259 | [0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,...] | |||
| 0.69314718055994530941723212145817657 | Logaritmus de 2 | L n ( 2 ) {\displaystyle Ln(2)} | ∑ n = 1 ∞ ( - 1 ) n + 1 n = 1 1 - 1 2 + 1 3 - 1 4 + 1 5 - ⋯ {\displaystyle \sum _{n=1}^{\infty }{\frac {(-)1)^{n+1}}{n}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\frac {1}{5}}-\cdots } | Součet[n=1 až ∞]{(-1)^(n+1)/n} | T | A002162 | [0;1,2,3,1,6,3,1,1,2,1,1,1,1,3,10,...] |
| 0.78343051071213440705926438652697546 | Sen druhého ročníku1 J.Bernoulli | I 1 {\displaystyle I_{1}} | ∑ n = 1 ∞ ( - 1 ) n + 1 n n = 1 - 1 2 2 + 1 3 3 - 1 4 4 + 1 5 5 + ... {\displaystyle \sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{n}}}=1-{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}-{\frac {1}{4^{4}}}+{\frac {1}{5^{5}}}+\dots } | Součet[ -(-1)^n /n^n] | T | A083648 | [0;1,3,1,1,1,1,1,1,2,4,7,2,1,2,1,1,1,...] |
| 0.78539816339744830961566084581987572 | Dirichletova beta(1) | β ( 1 ) {\displaystyle \beta (1)} | π 4 = ∑ n = 0 ∞ ( - 1 ) n 2 n + 1 = 1 1 - 1 3 + 1 5 - 1 7 + 1 9 - ⋯ {\displaystyle {\frac {\pi }{4}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{2n+1}}={\frac {1}{1}}-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}-\cdots } | Součet[n=0 až ∞]{(-1)^n/(2n+1)} | T | A003881 | [0; 1,3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,...] |
| 0.82246703342411321823620758332301259 | Obchodní cestující Nielsen-Ramanujan | ζ ( 2 ) 2 {\displaystyle {\frac {\zeta (2)}{2}} | π 2 12 = ∑ n = 1 ∞ ( - 1 ) n + 1 n 2 = 1 1 2 - 1 2 2 + 1 3 2 - 1 4 2 + 1 5 2 - ... {\displaystyle {\frac {\pi ^{2}}{12}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{2}}}={\frac {1}{1^{2}}}{-}{\frac {1}{2^{2}}}{+}{\frac {1}{3^{2}}}{-}{\frac {1}{4^{2}}}{+}{\frac {1}{5^{2}}}-\dots } | Součet[n=1 až ∞]{((-1)^(k+1))/n^2} | T | A072691 | [0;1,4,1,1,1,2,1,1,1,1,3,2,2,4,1,1,1,...] |
| 0.91596559417721901505460351493238411 | Katalánská konstanta | C {\displaystyle C} | ∑ n = 0 ∞ ( - 1 ) n ( 2 n + 1 ) 2 = 1 1 2 - 1 3 2 + 1 5 2 - 1 7 2 + ⋯ {\displaystyle \sum _{n=0}^{\infty }{\frac {(-)1)^{n}}{(2n+1)^{2}}}={\frac {1}{1^{2}}}-{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}-{\frac {1}{7^{2}}}+\cdots } | Součet[n=0 až ∞]{(-1)^n/(2n+1)^2} | I | A006752 | [0;1,10,1,8,1,88,4,1,1,7,22,1,2,...] |
| 1.05946309435929526456182529494634170 | Poměr vzdálenosti mezi půltóny | 2 12 {\displaystyle {\sqrt[{12}]{2}}} | 2 12 {\displaystyle {\sqrt[{12}]{2}}} | 2^(1/12) | I | A010774 | [1;16,1,4,2,7,1,1,2,2,7,4,1,2,1,60,1,3,1,2,...] |
| 1,.08232323371113819151600369654116790 | Zeta(04) | ζ 4 {\displaystyle \zeta {4}} | π 4 90 = ∑ n = 1 ∞ 1 n 4 = 1 1 4 + 1 2 4 + 1 3 4 + 1 4 4 + 1 5 4 + ... {\displaystyle {\frac {\pi ^{4}}{90}}=\sum _{n=1}^{\infty }{\frac {1}{n^{4}}}={\frac {1}{1^{4}}}+{\frac {1}{2^{4}}}+{\frac {1}{3^{4}}}+{\frac {1}{4^{4}}}+{\frac {1}{5^{4}}}+\dots } | Součet[n=1 až ∞]{1/n^4} | T | A013662 | [1;12,6,1,3,1,4,183,1,1,2,1,3,1,1,5,4,2,7,...] |
| 1.1319882487943 ... | Viswanaths konstantní | C V i {\displaystyle C_{Vi}} | lim n → ∞ | a n | 1 n {\displaystyle \lim _{n\to \infty }|a_{n}|^{\frac {1}{n}}}} | A078416 | [1;7,1,1,2,1,3,2,1,2,1,8,1,5,1,1,1,9,1,...] | ||
| 1.20205690315959428539973816151144999 | Apéry konstantní | ζ ( 3 ) {\displaystyle \zeta (3)} | ∑ n = 1 ∞ 1 n 3 = 1 1 3 + 1 2 3 + 1 3 3 + 1 4 3 + 1 5 3 + ⋯ {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{3}}}={\frac {1}{1^{3}}}+{\frac {1}{2^{3}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{3}}}+{\frac {1}{5^{3}}}+\cdots \,\! } | Součet[n=1 až ∞]{1/n^3} | I | A010774 | [1;4,1,18,1,1,1,4,1,9,9,2,1,1,1,2,...] |
| 1.22541670246517764512909830336289053 | Gama(3/4) | Γ ( 3 4 ) {\displaystyle \Gamma ({\tfrac {3}{4}})} | ( - 1 + 3 4 ) ! {\displaystyle \left(-1+{\frac {3}{4}}\right)! } | (-1+3/4)! | T | A068465 | [1;4,2,3,2,2,1,1,1,2,1,4,7,1,171,3,2,3,1,1,...] |
| 1.23370055013616982735431137498451889 | Favardova konstanta | 3 4 ζ ( 2 ) {\displaystyle {\tfrac {3}{4}}\zeta (2)} | π 2 8 = ∑ n = 0 ∞ 1 ( 2 n - 1 ) 2 = 1 1 2 + 1 3 2 + 1 5 2 + 1 7 2 + ... {\displaystyle {\frac {\pi ^{2}}{8}}=\sum _{n=0}^{\infty }{\frac {1}{(2n-1)^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}+\dots } | součet[n=1 až ∞]{1/((2n-1)^2)} | T | A111003 | [1;4,3,1,1,2,2,5,1,1,1,1,2,1,2,1,10,4,3,1,1,...] |
| 1.25992104989487316476721060727822835 | Kořen krychle 2, constante Delian | 2 3 {\displaystyle {\sqrt[{3}]{2}}} | 2 3 {\displaystyle {\sqrt[{3}]{2}}} | 2^(1/3) | I | A002580 | [1;3,1,5,1,1,4,1,1,8,1,14,1,10,...] |
| 1.29128599706266354040728259059560054 | Sen druhého ročníku2 J.Bernoulli | I 2 {\displaystyle I_{2}} | ∑ n = 1 ∞ 1 n n = 1 + 1 2 2 + 1 3 3 + 1 4 4 + 1 5 5 + 1 6 6 + ... {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{n}}}=1+{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{4}}}}+{\frac {1}{5^{5}}}+{\frac {1}{6^{6}}}+\dots } | Součet[1/(n^n]), {n, 1, ∞}] | A073009 | [1;3,2,3,4,3,1,2,1,1,6,7,2,5,3,1,2,1,8,1,...] | |
| 1.32471795724474602596090885447809734 | Plastové číslo | ρ {\displaystyle \rho } | 1 + 1 + 1 + 1 + ⋯ 3 3 3 3 {\displaystyle {\sqrt[{3}]{1+{\sqrt[{3}]{1+{\sqrt[{3}]{1+{\sqrt[{3}]{1+\cdots }}}}}}}}} | I | A060006 | [1;3,12,1,1,3,2,3,2,4,2,141,80,2,5,1,2,8,...] | |
| 1.41421356237309504880168872420969808 | Druhá odmocnina ze 2, Pythagorova konstanta | 2 {\displaystyle {\sqrt {2}}} | ∏ n = 1 ∞ 1 + ( - 1 ) n + 1 2 n - 1 = ( 1 + 1 1 ) ( 1 - 1 3 ) ( 1 + 1 5 ) . . . {\displaystyle \prod _{n=1}^{\infty }1+{\frac {(-1)^{n+1}}{2n-1}}=\levá(1{+}{\frac {1}{1}}}pravá)\levá(1{-}{\frac {1}{3}}}pravá)\levá(1{+}{\frac {1}{5}}}pravá)... } | prod[n=1 až ∞]{1+(-1)^(n+1)/(2n-1)} | I | A002193 | [1;2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,...] |
| 1.44466786100976613365833910859643022 | Steinerovo číslo | e 1 e {\displaystyle e^{\frac {1}{e}}} | e 1 / e {\displaystyle e^{1/e}} | A073229 | [1;2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...] | ||
| 1.53960071783900203869106341467188655 | Lieb's Square Ice constant | W 2 D {\displaystyle W_{2D}} | lim n → ∞ ( f ( n ) ) n - 2 = ( 4 3 ) 3 2 {\displaystyle \lim _{n\to \infty }(f(n))^{n^{-2}}=\left({\frac {4}{3}}\right)^{\frac {3}{2}}}} | (4/3)^(3/2) | I | A118273 | [1;1,1,5,1,4,2,1,6,1,6,1,2,4,1,5,1,1,2,...] |
| 1.57079632679489661923132169163975144 | Výrobek Wallis | π / 2 {\displaystyle \pi /2} | ∏ n = 1 ∞ ( 4 n 2 4 n 2 - 1 ) = 2 1 ⋅ 2 3 ⋅ 4 3 ⋅ 4 5 ⋅ 6 5 ⋅ 6 7 ⋅ 8 7 ⋅ 8 9 ⋯ {\displaystyle \prod _{n=1}^{\infty }\left({\frac {4n^{2}}{4n^{2}-1}}\pravo)={\frac {2}{1}}\cdot {\frac {2}{3}}\cdot {\frac {4}{3}}\cdot {\frac {4}{5}}\cdot {\frac {6}{5}}\cdot {\frac {6}{7}}\cdot {\frac {8}{7}}\cdot {\frac {8}{9}}\cdots } | T | A019669 | [1;1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1...] | |
| 1.60669515241529176378330152319092458 | Erdősova-Borweinova konstanta | E B {\displaystyle E_{\,B}} | ∑ n = 1 ∞ 1 2 n - 1 = 1 1 + 1 3 + 1 7 + 1 15 + ⋯ {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}={\frac {1}{1}}+{\frac {1}{3}}+{\frac {1}{7}}+{\frac {1}{15}}+\cdots \,\! } | sum[n=1 až ∞]{1/(2^n-1)} | I | A065442 | [1;1,1,1,1,5,2,1,2,29,4,1,2,2,2,2,6,1,7,1,...] |
| 1.61803398874989484820458633436563812 | Phi, zlatý řez | φ {\displaystyle \varphi } | 1 + 5 2 = 1 + 1 + 1 + 1 + ⋯ {\displaystyle {\frac {1+{\sqrt {5}}}{2}}={\sqrt {1+{\sqrt {1+{\sqrt {1+{\sqrt {1+\cdots }}}}}}}}} | (1+5^(1/2))/2 | I | A001622 | [0;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...] |
| 1.64493406684822643647241516664602519 | Zeta(2) | ζ ( 2 ) {\displaystyle \zeta (\,2)} | π 2 6 = ∑ n = 1 ∞ 1 n 2 = 1 1 2 + 1 2 2 + 1 3 2 + 1 4 2 + ⋯ {\displaystyle {\frac {\pi ^{2}}{6}}=\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{4^{2}}}+\cdots } | Součet[n=1 až ∞]{1/n^2} | T | A013661 | [1;1,1,1,4,2,4,7,1,4,2,3,4,10 1,2,1,1,1,15,...] |
| 1.66168794963359412129581892274995074 | Somosova kvadratická konstanta opakování | σ {\displaystyle \sigma } | 1 2 3 ⋯ = 1 1 / 2 ; 2 1 / 4 ; 3 1 / 8 ⋯ {\displaystyle {\sqrt {1{\sqrt {2{\sqrt {3\cdots }}}}}}=1^{1/2};2^{1/4};3^{1/8}\cdots } | T | A065481 | [1;1,1,1,21,1,1,1,6,4,2,1,1,2,1,3,1,13,13,...] | |
| 1.73205080756887729352744634150587237 | Theodorus konstanta | 3 {\displaystyle {\sqrt {3}}} | 3 {\displaystyle {\sqrt {3}}} | 3^(1/2) | I | A002194 | [1;1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,...] |
| 1.75793275661800453270881963821813852 | Kasnerovo číslo | R {\displaystyle R} | 1 + 2 + 3 + 4 + ⋯ {\displaystyle {\sqrt {1+{\sqrt {2+{\sqrt {3+{\sqrt {4+\cdots }}}}}}}}} | A072449 | [1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...] | ||
| 1.77245385090551602729816748334114518 | Carlson-Levin konstanta | Γ ( 1 2 ) {\displaystyle \Gamma ({\tfrac {1}{2}})} | π = ( - 1 2 ) ! {\displaystyle {\sqrt {\pi }}=\left(-{\frac {1}{2}}}\right)! } | sqrt (pí) | T | A002161 | [1;1,3,2,1,1,6,1,28,13,1,1,2,18,1,1,1,83,1,...] |
| 2.29558714939263807403429804918949038 | Univerzální parabolická konstanta | P 2 {\displaystyle P_{\,2}} | ln ( 1 + 2 ) + 2 {\displaystyle \ln(1+{\sqrt {2}})+{\sqrt {2}} | ln(1+sqrt 2)+sqrt 2 | T | A103710 | [2;3,2,1,1,1,1,3,3,1,1,4,2,3,2,7,1,6,1,8,...] |
| 2.30277563773199464655961063373524797 | Bronzové číslo | σ R r {\displaystyle \sigma _{\,Rr}} | 3 + 13 2 = 1 + 3 + 3 + 3 + 3 + ⋯ {\displaystyle {\frac {3+{\sqrt {13}}}{2}}=1+{\sqrt {3+{\sqrt {3+{\sqrt {3+{\sqrt {3+\cdots }}}}}}}}} | (3+sqrt 13)/2 | I | A098316 | [3;3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,...] |
| 2.37313822083125090564344595189447424 | Lévyho konstanta 2 | 2 ln γ {\displaystyle 2\,\ln \,\gamma } | π 2 6 ln ( 2 ) {\displaystyle {\frac {\pi ^{2}}{6\ln(2)}}} | Pi^(2)/(6*ln(2)) | T | A174606 | [2;2,1,2,8,57,9,32,1,1,2,1,2,1,2,1,2,1,3,2,...] |
| 2.50662827463100050241576528481104525 | odmocnina z 2 pí | 2 π {\displaystyle {\sqrt {2\pi }}} | 2 π = lim n → ∞ n ! e n n n n {\displaystyle {\sqrt {2\pi }}=\lim _{n\to \infty }{\frac {n!\;e^{n}}{n^{n}{\sqrt {n}}}}} | sqrt (2*pi) | T | A019727 | [2;1,1,37,4,1,1,1,1,9,1,1,2,8,6,1,2,2,1,3,...] |
| 2.66514414269022518865029724987313985 | Gelfond-Schneiderova konstanta | G G S {\displaystyle G_{_{\,GS}}} | 2 2 {\displaystyle 2^{\sqrt {2}}} | 2^sqrt{2} | T | A007507 | [2;1,1,1,72,3,4,1,3,2,1,1,1,14,1,2,1,1,3,1,...] |
| 2.68545200106530644530971483548179569 | Khintchin konstanta | K 0 {\displaystyle K_{\,0}} | ∏ n = 1 ∞ [ 1 + 1 n ( n + 2 ) ] ln n / ln 2 {\displaystyle \prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}}\right]^{\ln n/\ln 2}} | prod[n=1 až ∞]{(1+1/(n(n+2)))^((ln(n)/ln(2))} | ? | A002210 | [2;1,2,5,1,1,2,1,1,3,10,2,1,3,2,24,1,3,2,...] |
| 3.27582291872181115978768188245384386 | Khinchin-Lévyho konstanta | γ {\displaystyle \gamma } | e π 2 / ( 12 ln 2 ) {\displaystyle e^{\pi ^{2}/(12\ln 2)}} | e^(\pi^2/(12 ln(2)) | A086702 | [3;3,1,1,1,2,29,1,130,1,12,3,8,2,4,1,3,55,...] | |
| 3.35988566624317755317201130291892717 | Reciproční Fibonacciho konstanta | Ψ {\displaystyle \Psi } | ∑ n = 1 ∞ 1 F n = 1 1 + 1 1 + 1 2 + 1 3 + 1 5 + 1 8 + 1 13 + ⋯ {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{F_{n}}={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots } | A079586 | [3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...] | ||
| 4.13273135412249293846939188429985264 | Kořen 2 e pí | 2 e π {\displaystyle {\sqrt {2e\pi }}} | 2 e π {\displaystyle {\sqrt {2e\pi }}} | sqrt(2e pí) | T | A019633 | [4;7,1,1,6,1,5,1,1,1,8,3,1,2,2,15,2,1,1,2,4,...] |
| 6.58088599101792097085154240388648649 | Froda konstantní | 2 e {\displaystyle 2^{\,e}} | 2 e {\displaystyle 2^{e}} | 2^e | [6;1,1,2,1,1,2,3,1,14,11,4,3,1,1,7,5,5,2,7,...] | ||
| 9.86960440108935861883449099987615114 | Pí čtverec | π 2 {\displaystyle \pi ^{2}} | 6 ∑ n = 1 ∞ 1 n 2 = 6 1 2 + 6 2 2 + 6 3 2 + 6 4 2 + ⋯ {\displaystyle 6\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {6}{1^{2}}}}+{\frac {6}{2^{2}}}+{\frac {6}{3^{2}}}}+{\frac {6}{4^{2}}}+\cdots } | 6 Součet[n=1 až ∞]{1/n^2} | T | A002388 | [9;1,6,1,2,47,1,8,1,1,2,2,1,1,8,3,1,10,5,...] |
| 23.1406926327792690057290863679485474 | Gelfondova konstanta | e π {\displaystyle e^{\pi }} | ∑ n = 0 ∞ π n n ! = π 1 1 + π 2 2 ! + π 3 3 ! + π 4 4 ! + ⋯ {\displaystyle \sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}={\frac {\pi ^{1}}{1}}+{\frac {\pi ^{2}}{2!}}+{\frac {\pi ^{3}}{3!}}+{\frac {\pi ^{4}}{4!}}+\cdots } | Součet[n=0 až ∞]{(pi^n)/n!} | T | A039661 | [23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...] |
Odpověď: Matematická konstanta je číslo, které má zvláštní význam pro výpočty.
Odpověď: Příkladem matematické konstanty je ً, která představuje poměr obvodu kruhu k jeho průměru.
Odpověď: Ano, hodnota ً je pro každou kružnici vždy stejná.
Odpověď: Ne, matematické konstanty jsou obvykle reálná neintegrální čísla.
Odpověď: Matematické konstanty nepocházejí z fyzikálních měření jako fyzikální konstanty.
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![{\displaystyle \sum _{n=1}^{\infty }({-}1)^{n}(n^{1/n}{-}1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+{\sqrt[{4}]{4}}\,\dots }](https://www.alegsaonline.com/image/870bc7fa0415cfa4f3c3fb9253254c65e8e9d967.svg)
![{\displaystyle {\sqrt[{i}]{i}}=i^{-i}=i^{\frac {1}{i}}=(i^{i})^{-1}=e^{\frac {\pi }{2}}}](https://www.alegsaonline.com/image/904fff5ea95018fde18c45c94097a379edad291e.svg)
![{\displaystyle {\sqrt[{12}]{2}}}](https://www.alegsaonline.com/image/bc835f27425fb3140e1f75a5faa35b1e8b9efc35.svg)
![{\displaystyle {\sqrt[{3}]{2}}}](https://www.alegsaonline.com/image/9ca071ab504481c2bb76081aacb03f5519930710.svg)
![{\displaystyle {\sqrt[{3}]{1+{\sqrt[{3}]{1+{\sqrt[{3}]{1+{\sqrt[{3}]{1+\cdots }}}}}}}}}](https://www.alegsaonline.com/image/fe5c1cba04372927a214a2ce1b1d6b213bb12ee3.svg)
![{\displaystyle \prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\ln n/\ln 2}}](https://www.alegsaonline.com/image/cbfef25fcd2817842f1c50956dc798248c418be6.svg)
