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A113319 Decimal expansion of sum( k>=0, 1/(k^2+1) ). 6
2, 0, 7, 6, 6, 7, 4, 0, 4, 7, 4, 6, 8, 5, 8, 1, 1, 7, 4, 1, 3, 4, 0, 5, 0, 7, 9, 4, 7, 5, 0, 0, 0, 0, 4, 9, 0, 4, 4, 5, 6, 5, 6, 2, 6, 6, 4, 0, 3, 8, 1, 6, 6, 6, 5, 5, 7, 5, 0, 6, 2, 4, 8, 4, 3, 9, 0, 1, 5, 4, 2, 4, 7, 9, 1, 8, 3, 1, 0, 0, 2, 1, 7, 4, 3, 5, 6, 5, 5, 5, 1, 7, 5, 9, 3, 9, 5, 4, 9, 1, 8, 7, 6, 5, 1 (list; constant; graph; refs; listen; history; text; internal format)
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

CROSSREFS

Cf. A013661: sum( i>=1, 1/i^2 ); A232883: sum( i>=0, 1/(2*i^2+1) ). [Bruno Berselli, Dec 02 2013]

Cf. A248177.

Sequence in context: A104540 A228819 A178818 * A021832 A160509 A243444

Adjacent sequences:  A113316 A113317 A113318 * A113320 A113321 A113322

KEYWORD

nonn,cons

AUTHOR

Benoit Cloitre, Jan 07 2006

EXTENSIONS

Offset changed from 0 to 1 by Bruno Berselli, Dec 02 2013

STATUS

approved

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Last modified June 23 23:18 EDT 2017. Contains 288676 sequences.