A301814 Decimal expansion of Re((1/4)*Integral_{-infinity..+infinity} sqrt(log(1/2 + i*z))* sech(Pi*z)^2).

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

Offset

0,2

Comments

See the references given in A301815.

Links

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

Formula

Let beta(r) be the real part of Integral_{-oo..oo} (log(1/2 + i*z)^r / (exp(-Pi*z) + exp(Pi*z))^2) dz, where i denotes the imaginary unit. The constant equals beta(1/2) and A301815 equals -beta(1).

Example

Equals
0.03762549204826043264994372728978762248544767906044519708664851302092...

Maple

Re((1/2)*int(sqrt(log(1/2 + I*z))*sech(Pi*z)^2, z=0..64)): evalf(%, 100);

Crossrefs

Cf. A301815.

Sequence in context: A016666 A318352 A377805 * A065281 A256848 A019952

Adjacent sequences: A301811 A301812 A301813 * A301815 A301816 A301817

Keyword

nonn,cons

Author

Peter Luschny, Apr 13 2018

Status

approved