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Decimal expansion of the negated value of the digamma function at 1/10.
4

%I #42 Jun 02 2022 05:46:08

%S 1,0,4,2,3,7,5,4,9,4,0,4,1,1,0,7,6,7,9,5,1,6,8,2,1,6,2,1,9,0,1,0,0,2,

%T 5,4,0,4,2,9,1,6,4,2,5,6,2,4,4,4,1,8,8,9,2,0,3,2,6,3,9,2,0,8,4,1,0,8,

%U 8,6,7,9,1,0,8,8,1,5,2,6,2,7,0,2,3,1,5,3,9,8,3,4,9,1,2,1,9,9,2,7,9,8,0,8,2

%N Decimal expansion of the negated value of the digamma function at 1/10.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DigammaFunction.html">Digamma Function</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Digamma_function">Digamma function</a>

%H <a href="/index/Di#differential_equations">Index entries for sequences related to the digamma function</a>

%F Psi(1/10) = -gamma - Pi*5^(1/4)*(sqrt(2 + sqrt(5))/2) - 2*log(2) - 5*log(5)/4 - 3*sqrt(5)*log((1 + sqrt(5))/2)/2, where gamma is the Euler-Mascheroni constant A001620.

%F Equals gamma - H(-9/10), H(z) the harmonic number. - _Peter Luschny_, Aug 22 2019

%e Equals 10.4237549404110767951682162190100254042916425624441889203263920841...

%p evalf(-Psi(1/10), 102);

%t RealDigits[-PolyGamma[1/10], 10, 105][[1]]

%o (PARI) -psi(1/10)

%Y Cf. A020759, A047787, A020777, A200135, A222457, A250129.

%K nonn,cons

%O 2,3

%A _Vaclav Kotesovec_, Aug 22 2019