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A113319
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Decimal expansion of Sum_{k>=0} 1/(k^2+1).
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26
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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
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OFFSET
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1,1
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COMMENTS
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Known to be transcendental. After n=2 it is the same as A100554(n).
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REFERENCES
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Michel Waldschmidt, Elliptic functions and transcendance, Surveys in number theory, 143-188, Dev. Math., 17, Springer, New York, 2008.
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LINKS
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FORMULA
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Equals 1/2 + Pi / tanh(Pi) / 2.
Equals 1+Integral_{x >= 0} sin(x)/(exp(x)-1) dx. - Robert FERREOL, Jan 12 2016.
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EXAMPLE
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2.076674047468581174134050794750000490445656266403816665575062484390...
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MATHEMATICA
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RealDigits[N[Im[PolyGamma[0, I]], 105]][[1]] (* Vaclav Kotesovec, Oct 03 2014 *)
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PROG
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(PARI) 1/2+Pi/tanh(Pi)/2
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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