A282823 Decimal expansion of Pi^2 + 8*K, where K is Catalan's constant.
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, 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, 1, 4, 8, 9, 8, 0, 6, 2, 9, 2, 4, 3, 3, 9, 8, 8, 3, 6, 6, 2, 5, 5, 0, 7
Offset: 2
Examples
17.19732915450711073927131911933522402150689440149416770054533433319414...
Links
- G. C. Greubel, Table of n, a(n) for n = 2..10000
- Eric Weisstein's World of Mathematics, Polygamma Function (formula 24).
- Sheldon Yang, Some properties of Catalan's constant G, Internat. J. Math. Ed. Sci. Tech. 23 (4) (1992) 549-556.
Programs
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Magma
SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)^2 + 8*Catalan(R); // G. C. Greubel, Aug 24 2018
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Maple
Psi(1,1/4) ; evalf(%) # R. J. Mathar, Dec 04 2024
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Mathematica
RealDigits[Pi^2 + 8 Catalan, 10, 100][[1]]
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PARI
Pi^2 + 8*Catalan \\ Charles R Greathouse IV, Mar 04 2018
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PARI
zetahurwitz(2,1/4) \\ Charles R Greathouse IV, Mar 04 2018
Formula
Equals 16*A222183.
Equals Psi(1, 1/4), where Psi(r, x) is the Polygamma function of order r.
Equals Sum_{k>=0} 1/(k + 1/4)^2. - Amiram Eldar, May 17 2022