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

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Polygamma Function (formula 25).

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

Example

2.5418796476716064983976628804170782491205044129874135522813644192459406...

Mathematica

RealDigits[Pi^2 - 8 Catalan, 10, 100][[1]]

Prog

(PARI) Pi^2 - 8*Catalan \\ Charles R Greathouse IV, Jan 31 2018
(PARI) zetahurwitz(2, 3/4) \\ Charles R Greathouse IV, Jan 31 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)^2 - 8*Catalan(R); // G. C. Greubel, Aug 24 2018

Crossrefs

Cf. A000796, A006752, A247037, A173953/A173954, A282823.

Sequence in context: A254881 A100946 A200019 * A106664 A116516 A011417

Adjacent sequences: A282821 A282822 A282823 * A282825 A282826 A282827

Keyword

nonn,cons

Author

Bruno Berselli, Mar 06 2017

Status

approved