login
Decimal expansion of Pi^4/24.
6

%I #15 Sep 28 2022 14:03:25

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

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

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

%N Decimal expansion of Pi^4/24.

%C Volume of the 8-dimensional unit sphere.

%H G. C. Greubel, <a href="/A164108/b164108.txt">Table of n, a(n) for n = 1..10000</a>

%H Cornel Ioan Vălean, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.124.7.659">Problem 11993</a>, The American Mathematical Monthly, Vol. 124, No. 7 (2017), p. 659; <a href="https://doi.org/10.1080/00029890.2019.1574184">An Integral Related to Euler Sums</a>, Solution to Problem 11993 by Abdelhak Berkane, ibid., Vol. 126, No. 4 (2019), pp. 373-374.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Hypersphere.html">Hypersphere</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/N-sphere">n-sphere</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals A164109/8 = A092425/24 = A072691*A102753.

%F Pi^4/240 = -Integral_{x=0..1} log(1-x)*log(1+x)^2/x dx (Vălean, 2017). - _Amiram Eldar_, Mar 26 2022

%e 4.0587121264167682181850138620293796354053160696952259038...

%t RealDigits[Pi^4/24, 10, 100][[1]] (* _G. C. Greubel_, Apr 09 2017 *)

%o (PARI) Pi^4/24 \\ _G. C. Greubel_, Apr 09 2017

%Y Cf. A000796, A019699, A102753, A164103, A164105, A164106.

%K cons,nonn

%O 1,1

%A _R. J. Mathar_, Aug 10 2009