A193712 - OEIS

%I #32 Jun 23 2023 03:43:00

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

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

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

%N Decimal expansion of Pi*zeta(3)/4.

%C The absolute value of Integral_{x=0..Pi/2} x^2*log(2*cos(x)) dx.

%C The absolute value of (d/db(d^2/da^2(Integral_{x=0..Pi/2} cos(ax)*(2*cos(x))^b dx))).

%C The absolute value of (Pi/2)*(d/db(d^2/da^2(gamma(b+1)/gamma((b+a)/2+1)/gamma((b-a)/2+1))) at a=0 and b=0. - _Seiichi Kirikami_ and _Peter J. C. Moses_

%D I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th edition, 3.631.9

%H Masato Kobayashi, <a href="https://arxiv.org/abs/2108.01247">Integral representations for zeta(3) with the inverse sine function</a>, arXiv:2108.01247 [math.NT], 2021.

%F Equals A000796*A002117/4.

%F Equals 2 * Integral_{x=0..1} arcsin(x)^2*arccos(x)/x dx (Kobayashi, 2021). - _Amiram Eldar_, Jun 23 2023

%e 0.94409328404076973180...

%t RealDigits[ N[Pi Zeta[3]/4, 150]][[1]]

%Y Cf. A000796, A002117, A152584, A193713, A194655.

%K nonn,cons

%O 0,1

%A _Seiichi Kirikami_, Aug 31 2011