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Decimal expansion of Sum_{n>=1} (cos((n*Pi)/2) + sin((n*Pi)/2)) / sqrt(n).
0

%I #8 Nov 03 2020 07:56:56

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

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

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

%N Decimal expansion of Sum_{n>=1} (cos((n*Pi)/2) + sin((n*Pi)/2)) / sqrt(n).

%F Equals zeta(1/2, 1/4).

%e 0.2399635244956309553375743101605772258978644368017700426676289374...

%p evalf(Zeta(0, 1/2, 1/4)*10^86, 100):

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

%t RealDigits[Zeta[1/2, 1/4], 10, 100][[1]] (* _Vaclav Kotesovec_, Nov 03 2020 *)

%Y zeta(1/2, 1/k): A059750 (k=1), A113024 (k=2), this sequence (k=4).

%K nonn,cons

%O 0,1

%A _Peter Luschny_, Nov 03 2020