A377647 - OEIS

A377647

Decimal expansion of Pi^4/15 + Pi^2*log(2)^2/4 - log(2)^4/4 - 21*log(2)*zeta(3)/4 - 6*Li_4(1/2).

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

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OFFSET

0,2

REFERENCES

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.8, p. 47.

LINKS

Table of n, a(n) for n=0..99.

Michael I. Shamos, A catalog of the real numbers, (2007). See pp. 181-182.

FORMULA

Integral_{x=1..2} log(x)^3/(x - 1) [Levin] (see Finch).

Integral_{x=0..1} log(1 + x)^3/x (see Shamos).

EXAMPLE

0.142514197935710915708721501209652160895463410764...

MATHEMATICA

RealDigits[Pi^4/15+Pi^2Log[2]^2/4-Log[2]^4/4-21Log[2]Zeta[3]/4-6PolyLog[4, 1/2], 10, 100][[1]]

CROSSREFS

Cf. A002117, A002162, A002388, A092425, A099218.