cp's OEIS Frontend

A247042 Decimal expansion of delta_2 (negated), a constant associated with a certain two-dimensional lattice sum.

%I A247042 #12 Feb 16 2025 08:33:23
%S A247042 3,9,0,0,2,6,4,9,2,0,0,0,1,9,5,5,8,8,2,8,4,5,4,7,5,3,3,6,6,0,4,9,7,3,
%T A247042 2,1,9,2,0,9,0,4,7,8,5,6,4,7,7,5,3,7,3,8,8,0,2,3,5,6,0,5,6,5,0,7,4,3,
%U A247042 1,9,1,4,9,7,5,4,9,1,9,6,6,2,0,9,0,3,3,5,9,0,4,5,9,7,4,7,5,6,5,1,1,9
%N A247042 Decimal expansion of delta_2 (negated), a constant associated with a certain two-dimensional lattice sum.
%C A247042 This constant is named sigma(1/2) in the Borwein reference.
%D A247042 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 79.
%H A247042 D. Borwein, J. M. Borwein and R. Shail, <a href="http://dx.doi.org/10.1016/0022-247X(89)90032-2">Analysis of Certain Lattice Sums</a>, Journal of Mathematical Analysis and Applications, Volume 143, Issue 1, October 1989, Pages 126-137.
%H A247042 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/LatticeSum.html">Lattice Sum</a>
%H A247042 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/MadelungConstants.html">Madelung Constants</a>
%F A247042 delta_2 = 2*zeta(1/2)*(zeta(1/2, 1/4) - zeta(1/2, 3/4)), where zeta(s,a) gives the generalized Riemann zeta function.
%e A247042 -3.900264920001955882845475336604973219209047856477537388...
%t A247042 delta2 = 2*Zeta[1/2]*(Zeta[1/2, 1/4] - Zeta[1/2, 3/4]); RealDigits[delta2, 10, 102] // First
%o A247042 (PARI) 2*zeta(1/2)*(zetahurwitz(1/2,1/4)-zetahurwitz(1/2,3/4)) \\ _Charles R Greathouse IV_, Jan 31 2018
%Y A247042 Cf. A088537, A085469, A090734, A247040.
%K A247042 nonn,cons,easy
%O A247042 1,1
%A A247042 _Jean-François Alcover_, Sep 10 2014