OFFSET
1,1
COMMENTS
Known to be transcendental. After n=2 it is the same as A100554(n).
Imaginary part of psi(I) (for the real part, see A248177). - Stanislav Sykora, Oct 03 2014
REFERENCES
Michel Waldschmidt, Elliptic functions and transcendance, Surveys in number theory, 143-188, Dev. Math., 17, Springer, New York, 2008.
LINKS
Ivan Panchenko, Table of n, a(n) for n = 1..1000
Wikipedia, Digamma function
FORMULA
Equals 1/2 + Pi / tanh(Pi) / 2.
Equals 1+Integral_{x >= 0} sin(x)/(exp(x)-1) dx. - Robert FERREOL, Jan 12 2016.
EXAMPLE
2.076674047468581174134050794750000490445656266403816665575062484390...
MATHEMATICA
RealDigits[N[Im[PolyGamma[0, I]], 105]][[1]] (* Vaclav Kotesovec, Oct 03 2014 *)
PROG
(PARI) 1/2+Pi/tanh(Pi)/2
(PARI) imag(psi(I)) \\ - Stanislav Sykora, Oct 03 2014
(PARI) sumnumrat(1/(x^2+1), 0) \\ Charles R Greathouse IV, Jan 20 2022
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Benoit Cloitre, Jan 07 2006
EXTENSIONS
Offset changed from 0 to 1 by Bruno Berselli, Dec 02 2013
STATUS
approved