A152649 Decimal expansion of Pi^4/72.

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

Offset

1,2

Comments

A division by 2 is missing in Mező's penultimate formula on page 4.

Links

Muniru A Asiru, Table of n, a(n) for n = 1..2000

David Borwein and Jonathan M. Borwein, On an intriguing integral and some series related to zeta(4), Proc. Am. Math. Soc. 123 (1995), 1191-1198.

I. Gradshteyn and I. Ryzhik, Table of integrals, series, and products, Academic Press, 1980, page 7 (formulas from 0.233.3 to 0.233.5).

István Mező, Summation of Hyperharmonic Series, arXiv:0811.0042 [math.CO], 2008.

Index entries for transcendental numbers.

Formula

Equals A098198/2 = A092425/72.

Equals Sum_{j >= 1} H(j)/j^3 where H(j) = A001008(j)/A002805(j).

Equals 20*Sum_{j >= 1} (2*j)^(-4) (see Gradsteyn and Ryzhik in Links section). - A.H.M. Smeets, Sep 18 2018

Equals Sum_{k>=1} A048272(k)/k^2. - Amiram Eldar, Jan 25 2024

Example

1.352904042138922739395004620676459878468438689898408634603...

Maple

evalf(Pi^4/72, 120); # Muniru A Asiru, Sep 18 2018

Mathematica

RealDigits[Pi^4/72, 10, 120][[1]] (* Harvey P. Dale, Feb 10 2013 *)

Prog

(PARI) Pi^4/72 \\ Michel Marcus, Jul 07 2015

Crossrefs

Cf. A001008, A002805, A048272, A092425, A098198.

Sequence in context: A376262 A340510 A075626 * A385253 A327263 A186412

Adjacent sequences: A152646 A152647 A152648 * A152650 A152651 A152652

Keyword

cons,easy,nonn

Author

R. J. Mathar, Dec 10 2008

Status

approved