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Riemann Zeta Function zeta(4)

zeta(4) is the value of the Riemann zeta function at 4, given by

zeta(4)=sum_(k=1)^(infty)1/(k^4)
(1)
=(pi^4)/(90)
(2)
=1.082323233711138...
(3)

(OEIS A013662).

A binomial sum identity is

zeta(4)=(36)/(17)sum_(k=1)^infty1/(k^4(2k; k)),
(4)

where (2k; k) is a binomial coefficient (Borwein and Bradley 1996).

See also

Riemann Zeta Function

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References

Borwein, J. M. and Bradley, D. M. "Searching Symbolically for Apéry-Like Formulae for Values of the Riemann Zeta Function." ACM SIGSAM Bull. Algebraic Sym. Manip. 30, 2-7, 1996. https://arxiv.org/abs/math/0505093.National Institute of Standards and Technology. "Integer Arguments." §25.6(i) in Digital Library of Mathematical Functions. https://dlmf.nist.gov/25.6.E1.Sloane, N. J. A. Sequence A013662 in "The On-Line Encyclopedia of Integer Sequences."

Cite this as:

Weisstein, Eric W. "Riemann Zeta Function zeta(4)." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RiemannZetaFunctionZeta4.html

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