A257134 - OEIS

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A257134

Decimal expansion of Pi^4/45.

2, 1, 6, 4, 6, 4, 6, 4, 6, 7, 4, 2, 2, 2, 7, 6, 3, 8, 3, 0, 3, 2, 0, 0, 7, 3, 9, 3, 0, 8, 2, 3, 3, 5, 8, 0, 5, 5, 4, 9, 5, 0, 1, 9, 0, 3, 8, 3, 7, 4, 5, 3, 8, 1, 5, 3, 6, 5, 9, 5, 2, 4, 3, 0, 8, 8, 8, 2, 4, 1, 2, 3, 2, 3, 7, 3, 9, 3, 7, 6, 9, 3, 1, 1, 3, 8, 1, 9, 2, 7, 1, 8, 8, 3, 3, 9, 9, 8, 3, 4, 4, 6, 5, 9, 8

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OFFSET

1,1

REFERENCES

L. J. P. Kilford, Modular Forms: A Classical and Computational Introduction, Imperial College Press, 2008, p. 15.

LINKS

Table of n, a(n) for n=1..105.

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.

Index entries for transcendental numbers.

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

Cf. A013662, A092425, A257136.

Sequence in context: A193094 A021466 A286259 * A121403 A155550 A355642

Adjacent sequences: A257131 A257132 A257133 * A257135 A257136 A257137

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Apr 16 2015

STATUS

approved