A300707 Decimal expansion of Pi^4/96.

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

Offset

1,4

Comments

Also the sum of the series Sum_{n>=0} (1/(2*n+1)^4), whose value is obtained from zeta(4) given by L. Euler in 1735: Sum_{n>=0} (2*n+1)^(-s) = (1-2^(-s))*zeta(s).

For the partial sums of this series see A120269/A128493. - Wolfdieter Lang, Sep 02 2019

References

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.

Eric Weisstein's World of Mathematics, Dirichlet Lambda Function. See (6).

Index entries for transcendental numbers

Formula

Equals A092425/96. - Omar E. Pol, Mar 11 2018

Equals (15/16)*zeta(4) = (15/16)*A013662. - Wolfdieter Lang, Sep 02 2019

Equals Sum_{k>=1} 1/(2*k-1)^4. - Sean A. Irvine, Mar 25 2025

Equals lambda(4), where lambda is the Dirichlet lambda function. - Michel Marcus, Aug 15 2025

Example

1.0146780316041920545462534655073449088513290174238064...

Maple

evalf((1/96)*Pi^4, 120)

Mathematica

RealDigits[Pi^4/96, 10, 120][[1]]

Prog

(PARI) default(realprecision, 120); Pi^4/96
(MATLAB) format long; pi^4/96

Crossrefs

Cf. A013662, A092425, A111003, A120269, A128493, A300709, A300710, A300731.

Sequence in context: A006185 A169788 A369802 * A296183 A021876 A261491

Adjacent sequences: A300704 A300705 A300706 * A300708 A300709 A300710

Keyword

nonn,cons

Author

Iaroslav V. Blagouchine, Mar 11 2018

Status

approved