A301817 Decimal expansion of the real Stieltjes gamma function at x = 3/2, negated.

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

Offset

0,3

Comments

See A301816 for comments and references.

Links

Table of n, a(n) for n=0..86.

Formula

c = Re((4/5)*Pi*Integral_{-oo..oo} log(1/2+i*z)^(5/2)/(exp(-Pi*z)+exp(Pi*z))^2 dz) where i is the imaginary unit.

Example

c = 0.1061680251833883309118041161434553083606726463282760881731396491647151...

Maple

Sti := x -> (4*Pi/(x + 1))*int(log(1/2 + I*z)^(x + 1)/(exp(-Pi*z) + exp(Pi*z))^2, z=0..64): Sti(3/2): Re(evalf(%, 100)); # Note that this is an approximation which needs a larger domain of integration and higher precision if used for more values than are in the Data section.

Crossrefs

Cf. A301816.

Sequence in context: A093563 A081775 A156163 * A011300 A222068 A272055

Adjacent sequences: A301814 A301815 A301816 * A301818 A301819 A301820

Keyword

nonn,cons

Author

Peter Luschny, Apr 09 2018

Status

approved