

A247042


Decimal expansion of delta_2 (negated), a constant associated with a certain twodimensional 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
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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 126137.
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

JeanFrançois Alcover, Sep 10 2014


STATUS

approved



