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Decimal expansion of Integral_{x=0..1} -x*zeta(1 - x).
0

%I #11 Jul 16 2021 01:58:12

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

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

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

%N Decimal expansion of Integral_{x=0..1} -x*zeta(1 - x).

%e 0.736789911413448643988374575444321693365546569110...

%p Digits:=100: Int(-s*Zeta(1 - s), s=0..1): evalf(%*10^90):

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

%t ndig = 100; RealDigits[N[-Integrate[x*Zeta[1 - x], {x, 0, 1}], ndig + 1], 10, ndig][[1]] (* _Amiram Eldar_, Jul 15 2021 *)

%o (PARI) intnum(x=0, 1, -x*zeta(1-x)) \\ _Michel Marcus_, Jul 15 2021

%K nonn,cons

%O 0,1

%A _Peter Luschny_, Jul 15 2021