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.
%I A247043 #11 Feb 16 2025 08:33:23 %S A247043 6,7,0,9,0,8,3,0,7,8,8,2,4,7,8,8,0,6,0,8,5,2,7,1,5,9,9,2,5,3,8,5,3,4, %T A247043 2,6,8,1,6,2,6,0,9,7,1,7,9,7,6,7,2,5,3,5,0,5,8,3,6,1,7,6,7,5,0,0,0,7, %U A247043 0,3,2,9,9,9,4,3,6,8,4,9,8,6,2,5,8,2,4,1,4,7,5,3,0,8,5,9,6,1,9,4,5,5,4 %N A247043 Decimal expansion of gamma_2, a lattice sum constant, analog of Euler's constant for two-dimensional lattices. %D A247043 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 80. %H A247043 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LatticeSum.html">Lattice Sum</a>. %F A247043 gamma_2 = (1/4)*(delta_2 + 2*log((sqrt(2) + 1)/(sqrt(2) - 1)) - 4*EulerGamma), where delta_2 is A247042. %e A247043 -0.670908307882478806085271599253853426816260971797672535... %t A247043 delta2 = 2*Zeta[1/2]*(Zeta[1/2, 1/4] - Zeta[1/2, 3/4]); gamma2 = (1/4)*(delta2 + 2*Log[(Sqrt[2] + 1)/(Sqrt[2] - 1)] - 4*EulerGamma); RealDigits[gamma2, 10, 103] // First %o A247043 (PARI) (2*zeta(1/2)*(zetahurwitz(1/2, 1/4)-zetahurwitz(1/2, 3/4)) + 2*log((sqrt(2) + 1)/(sqrt(2) - 1)))/4 - Euler \\ _Charles R Greathouse IV_, Jan 31 2018 %Y A247043 Cf. A247042. %K A247043 nonn,cons,easy %O A247043 0,1 %A A247043 _Jean-François Alcover_, Sep 10 2014