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A247042 Decimal expansion of delta_2 (negated), a constant associated with a certain two-dimensional lattice sum. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
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 A272535

Adjacent sequences:  A247039 A247040 A247041 * A247043 A247044 A247045

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Sep 10 2014

STATUS

approved

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Last modified January 18 20:57 EST 2019. Contains 319282 sequences. (Running on oeis4.)