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A248176
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Decimal expansion of psi(-1/2).
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2
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3, 6, 4, 8, 9, 9, 7, 3, 9, 7, 8, 5, 7, 6, 5, 2, 0, 5, 5, 9, 0, 2, 3, 6, 6, 7, 0, 0, 1, 2, 4, 4, 4, 3, 2, 8, 0, 6, 8, 4, 0, 3, 9, 5, 3, 3, 9, 5, 6, 5, 8, 9, 2, 9, 5, 2, 8, 7, 2, 7, 4, 6, 1, 2, 8, 3, 4, 5, 0, 2, 9, 2, 8, 2, 9, 4, 5, 8, 9, 7, 8, 5, 1, 3, 2, 6, 2, 8, 2, 7, 1, 5, 4, 1, 5, 8, 7, 5, 4, 0, 1, 3, 6, 5, 5, 9, 0
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OFFSET
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-1,1
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COMMENTS
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Psi denotes the digamma function.
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LINKS
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FORMULA
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Equals 2 + psi(1/2) = 2 - 2*log(2) - EulerGamma = 2 - A020759, (since psi(1 + x) = psi(x) + 1/x).
Equals Sum_{k>=1} (zeta(2*k+1)-1)/((k+1)*(2*k+1)). - Amiram Eldar, May 24 2021
Equals 4*Pi*Integral_{x>=0} (log(1 + i*x) / (exp(-Pi*x) + exp(Pi*x))^2). - Peter Luschny, Aug 04 2021
Equals lim_{n->oo} (log(n) - Sum_{k=1..n} 1/(k+1/2)). - Amiram Eldar, Mar 04 2023
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EXAMPLE
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0.0364899739785765205590236670012444328068403953395658929528727461...
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MATHEMATICA
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RealDigits[2 - (EulerGamma + 2Log[2]), 10, 100][[1]] (* Alonso del Arte, Oct 03 2014 *)
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PROG
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(PARI) psi(-1/2)
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 2 - (2*Log(2) + EulerGamma(R)); // G. C. Greubel, Aug 30 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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