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A200135 Decimal expansion of the negated value of the digamma function at 1/5.

%I A200135 #22 Sep 08 2022 08:46:00
%S A200135 5,2,8,9,0,3,9,8,9,6,5,9,2,1,8,8,2,9,5,5,4,7,2,0,7,9,6,2,4,4,9,9,5,2,
%T A200135 1,0,4,8,2,5,5,8,8,2,7,4,2,0,6,6,4,2,8,1,0,1,7,5,8,5,8,6,6,4,1,9,1,6,
%U A200135 2,4,7,5,4,0,9,1,6,1,9,6,5,2,5,4,6,5,7,7,8,2,4,3,1,9,5,7,0,3,6,2,4,1,2,4,0
%N A200135 Decimal expansion of the negated value of the digamma function at 1/5.
%H A200135 G. C. Greubel, <a href="/A200135/b200135.txt">Table of n, a(n) for n = 1..10000</a>
%H A200135 Wikipedia, <a href="http://en.wikipedia.org/wiki/Digamma_function">Digamma function</a>
%H A200135 <a href="/index/Di#differential_equations">Index entries for sequences related to the digamma function</a>
%F A200135 Psi(1/5) = -gamma - Pi*sqrt(1 + 2/sqrt(5))/2 - 5*log(5)/4 -sqrt(5)*log((3 + sqrt(5))/2)/4 where gamma = A001620, sqrt(1 + 2/sqrt(5)) = A019952, (3 + sqrt(5))/2 = A104457.
%e A200135 Psi(1/5) =  -5.289039896592188295547207962...
%p A200135 -gamma-Pi*sqrt(1+2/sqrt(5))/2-5*log(5)/4-sqrt(5)/4*log((3+sqrt(5)/2) ); evalf(%) ;
%t A200135 RealDigits[-PolyGamma[1/5], 10, 105] // First (* _Jean-François Alcover_, Feb 11 2013 *)
%o A200135 (PARI) -psi(1/5) \\ _Charles R Greathouse IV_, Jul 19 2013
%o A200135 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); -EulerGamma(R) -Pi(R)*Sqrt(1+2/Sqrt(5))/2 -5*Log(5)/4 -Sqrt(5)/4*Log((3+Sqrt(5)/2) ); // _G. C. Greubel_, Sep 03 2018
%Y A200135 Cf. A020759, A047787, A020777, A200064, A200134, A200136, A200137, A200138.
%K A200135 cons,nonn
%O A200135 1,1
%A A200135 _R. J. Mathar_, Nov 13 2011
%E A200135 More terms from _Jean-François Alcover_, Feb 11 2013