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A200134
Decimal expansion of the negated value of the digamma function at 3/4.
8
1, 0, 8, 5, 8, 6, 0, 8, 7, 9, 7, 8, 6, 4, 7, 2, 1, 6, 9, 6, 2, 6, 8, 8, 6, 7, 6, 2, 8, 1, 7, 1, 8, 0, 6, 9, 3, 1, 7, 0, 0, 7, 5, 0, 3, 9, 3, 3, 3, 1, 3, 6, 4, 5, 0, 6, 8, 0, 3, 3, 4, 9, 6, 7, 2, 1, 1, 1, 4, 0, 3, 8, 9, 5, 4, 3, 6, 4, 4, 3, 1, 8, 4, 4, 0, 5, 1, 9, 6, 3, 1, 6, 0, 9, 9, 4, 4
OFFSET
1,3
FORMULA
Psi(3/4) = -gamma + Pi/2 - 3*log(2) = A000796 - A020777 = 3.14159... - 4.22745...
Pi = gamma(0,1/4) - gamma(0,3/4) = A020777 - A200134, where gamma(n,x) denotes the generalized Stieltjes constants. - Peter Luschny, May 16 2018
EXAMPLE
Psi(3/4) = -1.085860879786472169626886762817...
MAPLE
evalf(-gamma+Pi/2-3*log(2)) ;
MATHEMATICA
RealDigits[ -PolyGamma[3/4], 10, 97] // First (* Jean-François Alcover, Feb 20 2013 *)
N[StieltjesGamma[0, 3/4], 99] (* Peter Luschny, May 16 2018 *)
PROG
(PARI) -psi(3/4) \\ Charles R Greathouse IV, Nov 22 2011
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); -EulerGamma(R) + Pi(R)/2 - 3*Log(2); // G. C. Greubel, Aug 29 2018
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
R. J. Mathar, Nov 13 2011
STATUS
approved