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

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, 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, 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

Offset: 1

Author

Jean-François Alcover, Sep 10 2014

Keywords

• nonn
• cons
• easy

Comments

This constant is named sigma(1/2) in the Borwein reference.

Examples

			-3.900264920001955882845475336604973219209047856477537388...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 79.

Links

• D. Borwein, J. M. Borwein and R. Shail, Analysis of Certain Lattice Sums, Journal of Mathematical Analysis and Applications, Volume 143, Issue 1, October 1989, Pages 126-137.
• Eric Weisstein's MathWorld, Lattice Sum
• Eric Weisstein's MathWorld, Madelung Constants

Crossrefs

Cf. A088537, A085469, A090734, A247040.

Programs

Mathematica

delta2 = 2*Zeta[1/2]*(Zeta[1/2, 1/4] - Zeta[1/2, 3/4]); RealDigits[delta2, 10, 102] // First

PARI

2*zeta(1/2)*(zetahurwitz(1/2,1/4)-zetahurwitz(1/2,3/4)) \\ Charles R Greathouse IV, Jan 31 2018

Formula

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.