A337711 Decimal expansion of (7/120)*Pi^4 = (21/4)*zeta(4).

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, 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, 3, 3, 2, 3, 4, 9, 8, 1, 5, 8

Offset: 1

Author

Wolfdieter Lang, Sep 16 2020

Keywords

• nonn
• cons

Comments

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.

Examples

			5.68219697698347550545901940684113148956744249757331626533562...
		

References

• L. D. Landau and E. M. Lifschitz, Band V, Statistische Physik, Akademie Verlag, 1966, eq. (1) for x=4, p. 172.

Links

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• Index entries for transcendental numbers

Crossrefs

Cf. A013662, A231535 (Planck, Bose-Einstein integral).

Programs

Mathematica

RealDigits[7*Pi^4/120, 10, 100][[1]] (* Amiram Eldar, May 27 2021 *)

Formula

Equals -Integral_{x=0..1} log(x)^3/(x+1) dx. - Amiram Eldar, May 27 2021