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%I #14 Oct 01 2022 15:43:46
%S 5,6,8,2,1,9,6,9,7,6,9,8,3,4,7,5,5,0,5,4,5,9,0,1,9,4,0,6,8,4,1,1,3,1,
%T 4,8,9,5,6,7,4,4,2,4,9,7,5,7,3,3,1,6,2,6,5,3,3,5,6,2,5,1,3,1,0,8,1,6,
%U 3,3,2,3,4,9,8,1,5,8
%N Decimal expansion of (7/120)*Pi^4 = (21/4)*zeta(4).
%C Equals Integral_{0..infinity} x^3/(exp(x) + 1) dx = (7/120)*Pi^4 = (21/4)*A013662. (Fermi-Dirac). See Abramowitz-Stegun, 23.2.8, for s=4, p. 807, and Landau-Lifschitz, eq. (1), for x=4, p. 172.
%D L. D. Landau and E. M. Lifschitz, Band V, Statistische Physik, Akademie Verlag, 1966, eq. (1) for x=4, p. 172.
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP?Res=150&Page=807&Submit=Go">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals -Integral_{x=0..1} log(x)^3/(x+1) dx. - _Amiram Eldar_, May 27 2021
%e 5.68219697698347550545901940684113148956744249757331626533562...
%t RealDigits[7*Pi^4/120, 10, 100][[1]] (* _Amiram Eldar_, May 27 2021 *)
%Y Cf. A013662, A231535 (Planck, Bose-Einstein integral).
%K nonn,cons
%O 1,1
%A _Wolfdieter Lang_, Sep 16 2020