A300709 - OEIS

A300709

Decimal expansion of Pi^6/960.

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

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OFFSET

1,5

COMMENTS

Also the sum of the series Sum_{n>=0} (1/(2n+1)^6), whose value is obtained from zeta(6) given by L. Euler in 1735: Sum_{n>=0}(2n+1)^(-s) = (1-2^(-s))*zeta(s).

REFERENCES

Stephen Hawking, God Created the Integers: The Mathematical Breakthroughs That Changed History, Running Press, 2007. See p. 397.

Konrad Knopp, Theory and application of infinite series, Blackie & Son Limited, London and Glasgow, 1954. See p. 238.

LINKS

Table of n, a(n) for n=1..103.

Index entries for transcendental numbers

FORMULA

Equals A092732/960. - Omar E. Pol, Mar 11 2018

From Artur Jasinski, Jun 24 2025: (Start)

Equals DirichletL(2,1,6).

Equals DirichletL(4,1,6).

Equals DirichletL(8,1,6).