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A259281 Decimal expansion of Sum'_{(x,y,z)=-infinity..infinity} 1/(x^2+y^2+z^2)^2, where the 'prime' indicates that the term x=y=z=0 is to be left out. 1
1, 6, 5, 3, 2, 3, 1, 5, 9, 5, 9, 7, 6, 1, 6, 6, 9, 6, 4, 3, 8, 9, 2, 7, 0, 4, 5, 9, 2, 8, 8, 7, 8, 5, 1, 7, 4, 3, 8, 3, 4, 1, 2, 9, 0, 7, 0, 2, 5, 5, 1, 8, 6, 8, 8, 6, 1, 1, 7, 7, 9, 3, 6, 5, 9, 5, 6, 0, 2, 7, 0, 3, 0, 9, 4, 9, 5, 1, 0, 8, 5, 2, 3, 0, 7, 7, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Jon E. Schoenfield, Table of n, a(n) for n = 2..401

M. Kontsevich and D. Zagier, Periods, Institut des Hautes Etudes Scientifiques 2001 IHES/M/01/22 p. 25.

Jon E. Schoenfield, Magma program

I. J. Zucker, Madelung constants and lattice sums for invariant cubic lattice complexes and certain tetragonal structures, J. Phys. A: Math. Gen. 8 (1975) 1734, Table 4, s=2, a(2s).

EXAMPLE

16.532315959761669643892704592887851743834129...

MATHEMATICA

(* This script gives only 10 correct digits *) s1 = NSum[(-2 + Pi*x*(Coth[Pi*x] + Pi*x*Csch[Pi*x]^2))/(4*x^4), {x, 1, Infinity} ]; s2 = NSum[-((Csch[Pi*x]^2*(2 + 2*Pi^2*x^2 - 2*Cosh[2*Pi*x] + Pi*x*Sinh[2*Pi*x]))/(16*x^4)), {x, 1, Infinity} ]; f[y_?NumericQ] := NSum[(Pi*Coth[Pi*Sqrt[x^2 + y^2]])/(4*(x^2 + y^2)^(3/2)), {x, 1, Infinity} ]; s3 = NSum[f[y], {y, 1, Infinity} ]; g[y_?NumericQ] := NSum[2*((Pi^2*x^2*Csch[Pi*Sqrt[x^2 + y^2]]^2)/(4*(x^2 + y^2)^2)), {x, 1, Infinity} ]; s4 = NSum[g[y], {y, 1, Infinity} ]; s = Pi^4/15 + 12*s1 + 8*(s2 + s3 + s4); RealDigits[s, 10, 10] // First

CROSSREFS

Sequence in context: A140684 A245632 A158038 * A153330 A225661 A225662

Adjacent sequences:  A259278 A259279 A259280 * A259282 A259283 A259284

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Jun 23 2015

STATUS

approved

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)