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

1,1

Comments

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

References

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

Links

Table of n, a(n) for n=1..102.

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

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.

Example

-3.900264920001955882845475336604973219209047856477537388...

Mathematica

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

Prog

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

Crossrefs

Cf. A088537, A085469, A090734, A247040.

Sequence in context: A058847 A088110 A122759 * A274400 A200495 A329937

Adjacent sequences: A247039 A247040 A247041 * A247043 A247044 A247045

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 10 2014

Status

approved