cp's OEIS Frontend

A152649 Decimal expansion of Pi^4/72.

%I A152649 #40 Jan 25 2024 02:44:36
%S A152649 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,
%T A152649 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,
%U A152649 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
%N A152649 Decimal expansion of Pi^4/72.
%C A152649 A division by 2 is missing in Mezo's penultimate formula on page 4.
%H A152649 Muniru A Asiru, <a href="/A152649/b152649.txt">Table of n, a(n) for n = 1..2000</a>
%H A152649 David Borwein and J. M. Borwein, <a href="http://dx.doi.org/10.1090/S0002-9939-1995-1231029-X">On an intriguing integral and some series related to zeta(4)</a>, Proc. Am. Math. Soc. 123 (1995), 1191-1198.
%H A152649 I. Gradsteyn and I. Ryzhik, <a href="http://mathtable.com/gr/index.html">Table of integrals, series and products</a>, Academic Press, 1980, page 7 (formulas from 0.233.3 to 0.233.5).
%H A152649 Istvan Mezo, <a href="http://arxiv.org/abs/0811.0042">Summation of Hyperharmonic Numbers</a>, arXiv:0811.0042 [math.CO], 2008.
%H A152649 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A152649 Equals A098198/2 = A092425/72.
%F A152649 Equals Sum_{j >= 1} H(j)/j^3 where H(j) = A001008(j)/A002805(j).
%F A152649 Equals 20*Sum_{j >= 1} (2*j)^(-4) (see Gradsteyn and Ryzhik in Links section). - _A.H.M. Smeets_, Sep 18 2018
%F A152649 Equals Sum_{k>=1} A048272(k)/k^2. - _Amiram Eldar_, Jan 25 2024
%e A152649 Equals 1.352904042138922739395004620676459878468438689898408634603...
%p A152649 evalf(Pi^4/72,120); # _Muniru A Asiru_, Sep 18 2018
%t A152649 RealDigits[Pi^4/72,10,120][[1]] (* _Harvey P. Dale_, Feb 10 2013 *)
%o A152649 (PARI) Pi^4/72 \\ _Michel Marcus_, Jul 07 2015
%Y A152649 Cf. A001008, A002805, A048272, A092425, A098198.
%K A152649 cons,easy,nonn
%O A152649 1,2
%A A152649 _R. J. Mathar_, Dec 10 2008