login
Decimal expansion of Gamma(3/2) * zeta(3/2).
0

%I #6 Mar 20 2024 04:36:51

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

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

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

%N Decimal expansion of Gamma(3/2) * zeta(3/2).

%F Equals Pochhammer(1, 1/2) * zeta(3/2, 1).

%F Equals sqrt(Pi/4) * zeta(3/2).

%F Equals Integral_{x>=0} sqrt(x) / (exp(x) - 1).

%F Equals A019704 * A078434.

%e 2.3151573733941170004258194691179813666769281990...

%p DecimalExpansion := proc(f, prec)

%p Digits := prec + 10: evalf(f, Digits) * 10^prec:

%p ListTools:-Reverse(convert(floor(%), base, 10)) end:

%p DecimalExpansion(sqrt(Pi/4)*Zeta(3/2), 100);

%t RealDigits[Pochhammer[1, 1/2] Zeta[3/2, 1], 10, 100][[1]]

%Y Cf. A019704, A078434.

%K nonn,cons

%O 1,1

%A _Peter Luschny_, Mar 19 2024