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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 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.)