OFFSET
1,1
REFERENCES
L. J. P. Kilford, Modular Forms: A Classical and Computational Introduction, Imperial College Press, 2008, p. 15.
LINKS
Alain Tissier, Apéry's Constant, Solution to Problem 10635, The American Mathematical Monthly, Vol. 106, No. 10 (1999), pp. 965-966.
Eric Weisstein's World of Mathematics, Eisenstein Series.
FORMULA
Pi^4/45 = 2*zeta(4) = G_4(infinity), where the function G_k(z) is the Eisenstein nonzero modular form of weight k.
Equals -Integral_{x=0..1} log(x)^2 * log(1 - x)/x dx. - Amiram Eldar, Jul 21 2020
Equals Sum_{n,m>=1} (Pi^2/6 - Sum_{k=1..n+m} 1/k^2)/(n*m) (Tissier, 1999). - Amiram Eldar, Jan 27 2024
EXAMPLE
2.16464646742227638303200739308233580554950190383745381536595243...
MATHEMATICA
RealDigits[Pi^4/45, 10, 105] // First
PROG
(PARI) Pi^4/45 \\ Charles R Greathouse IV, Oct 01 2022
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Apr 16 2015
STATUS
approved