cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A282823 Decimal expansion of Pi^2 + 8*K, where K is Catalan's constant.

This page as a plain text file.
%I A282823 #30 Feb 16 2025 08:33:42
%S A282823 1,7,1,9,7,3,2,9,1,5,4,5,0,7,1,1,0,7,3,9,2,7,1,3,1,9,1,1,9,3,3,5,2,2,
%T A282823 4,0,2,1,5,0,6,8,9,4,4,0,1,4,9,4,1,6,7,7,0,0,5,4,5,3,3,4,3,3,3,1,9,4,
%U A282823 1,4,8,9,8,0,6,2,9,2,4,3,3,9,8,8,3,6,6,2,5,5,0,7
%N A282823 Decimal expansion of Pi^2 + 8*K, where K is Catalan's constant.
%H A282823 G. C. Greubel, <a href="/A282823/b282823.txt">Table of n, a(n) for n = 2..10000</a>
%H A282823 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolygammaFunction.html">Polygamma Function</a> (formula 24).
%H A282823 Sheldon Yang, <a href="https://dx.doi.org/10.1080/0020739X.1192.10715688">Some properties of Catalan's constant G</a>, Internat. J. Math. Ed. Sci. Tech. 23 (4) (1992) 549-556.
%F A282823 Equals 16*A222183.
%F A282823 Equals Psi(1, 1/4), where Psi(r, x) is the Polygamma function of order r.
%F A282823 Equals Sum_{k>=0} 1/(k + 1/4)^2. - _Amiram Eldar_, May 17 2022
%e A282823 17.19732915450711073927131911933522402150689440149416770054533433319414...
%p A282823 Psi(1,1/4) ; evalf(%) # _R. J. Mathar_, Dec 04 2024
%t A282823 RealDigits[Pi^2 + 8 Catalan, 10, 100][[1]]
%o A282823 (PARI) Pi^2 + 8*Catalan \\ _Charles R Greathouse IV_, Mar 04 2018
%o A282823 (PARI) zetahurwitz(2,1/4) \\ _Charles R Greathouse IV_, Mar 04 2018
%o A282823 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)^2 + 8*Catalan(R); // _G. C. Greubel_, Aug 24 2018
%Y A282823 Cf. A000796, A006752, A222183, A282824.
%K A282823 nonn,cons
%O A282823 2,2
%A A282823 _Bruno Berselli_, Mar 06 2017