A282824 Decimal expansion of Pi^2 - 8*K, where K is Catalan's constant.
2, 5, 4, 1, 8, 7, 9, 6, 4, 7, 6, 7, 1, 6, 0, 6, 4, 9, 8, 3, 9, 7, 6, 6, 2, 8, 8, 0, 4, 1, 7, 0, 7, 8, 2, 4, 9, 1, 2, 0, 5, 0, 4, 4, 1, 2, 9, 8, 7, 4, 1, 3, 5, 5, 2, 2, 8, 1, 3, 6, 4, 4, 1, 9, 2, 4, 5, 9, 4, 0, 6, 6, 4, 2, 0, 9, 1, 6, 7, 0, 8, 7, 1, 6, 6, 9, 2, 1, 3, 0, 0, 3
Offset: 1
Examples
2.5418796476716064983976628804170782491205044129874135522813644192459406...
Links
- G. C. Greubel, Table of n, a(n) for n = 1..10000
- Ernst D. Krupnikov and K. S. Kolbig, Some special cases of the generalized hypergeometric function _{q+1}F_q, J. Comp. Appl. Math. 78 (1997) 79-95
- Eric Weisstein's World of Mathematics, Polygamma Function (formula 25).
- Sheldon Yang, Some properties of Catalan's constant G, Internat. J. Math. Ed. Sci. Tech. 23 (4) (1992) 549-556
Programs
-
Magma
SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)^2 - 8*Catalan(R); // G. C. Greubel, Aug 24 2018
-
Mathematica
RealDigits[Pi^2 - 8 Catalan, 10, 100][[1]]
-
PARI
Pi^2 - 8*Catalan \\ Charles R Greathouse IV, Jan 31 2018
-
PARI
zetahurwitz(2,3/4) \\ Charles R Greathouse IV, Jan 31 2018
Formula
Equals 16*A247037.
Equals Psi(1, 3/4), where Psi(r, x) is the Polygamma function of order r.
Because this equals Zeta(2, 3/4), with the Hurwitz Zeta function, this is the value of the series Sum_{k>=0} 1/(k + 3/4)^2 = 16*Sum_{k>=0} 1/(4*k+3)^2 with partial sums {A173953/(n+2) / A173954(n+2)}{n>=0}. - _Wolfdieter Lang, Nov 14 2017