OFFSET
0,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.7 Catalan's constant p. 55.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
FORMULA
Equals Pi^2/16 - G/2, where G is Catalan's constant.
Equals zeta(2, 3/4)/16 = Psi(1, 3/4)/16, with the Hurwitz zeta function and the Trigamma function Psi(1, z), and the partial sums of the series given in the name are {A173955(n+2) / A173954(n+2)}_{n>=0}. - Wolfdieter Lang, Nov 14 2017
Equals Integral_{x=1..oo} log(x)/(x^4 - 1) dx. - Amiram Eldar, Jul 17 2020
EXAMPLE
0.158867477979475406149853930026067390570031525811713347...
MATHEMATICA
RealDigits[Pi^2/16 - Catalan/2 , 10, 103] // First
PROG
(PARI) Pi^2/16 - Catalan/2 \\ Charles R Greathouse IV, Jan 30 2018
(PARI) zetahurwitz(2, 3/4)/16 \\ Charles R Greathouse IV, Jan 30 2018
(PARI) sumpos(k=0, 1/(4*k+3)^2) \\ Charles R Greathouse IV, Jan 30 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (Pi(R)^2 - 8*Catalan(R))/16; // G. C. Greubel, Aug 24 2018
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Sep 10 2014
STATUS
approved