A335415 Decimal expansion of Sum_{k>=0} 1/cosh(Pi*k).
1, 0, 9, 0, 1, 7, 0, 2, 9, 9, 5, 0, 8, 0, 4, 8, 1, 1, 3, 0, 2, 2, 6, 6, 8, 9, 7, 0, 2, 7, 9, 2, 4, 4, 2, 9, 3, 6, 1, 6, 8, 5, 8, 3, 1, 7, 4, 4, 0, 7, 2, 3, 6, 4, 9, 7, 5, 7, 9, 3, 2, 1, 9, 9, 7, 0, 2, 1, 5, 2, 0, 9, 0, 3, 6, 0, 3, 5, 7, 8, 9, 7, 4, 8, 9, 2, 2, 9, 3, 0, 8, 0, 9, 7, 9, 0, 3, 9, 7, 7, 1, 0, 4, 7, 2
Offset: 1
Examples
1.090170299508048113022668970279244293616858317440723649757932199702152...
Programs
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Maple
evalf(Sum(1/cosh(Pi*k), k=0..infinity), 120); evalf(1/2 + sqrt(Pi) / (2*GAMMA(3/4)^2), 120);
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Mathematica
RealDigits[1/2 + Gamma[1/4]^2/(4*Pi^(3/2)), 10, 120][[1]]
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PARI
suminf(k=0, 1/cosh(Pi*k))
Formula
Equals 1/2 + Gamma(1/4)^2 / (4*Pi^(3/2)).
Equals 1/2 + sqrt(Pi) / (2*Gamma(3/4)^2).