A264156 - OEIS

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A264156

Decimal expansion of M_5, the 5-dimensional analog of Madelung's constant (negated).

1, 9, 0, 9, 3, 3, 7, 8, 1, 5, 6, 1, 8, 7, 6, 8, 5, 5, 9, 5, 2, 0, 1, 4, 3, 7, 9, 8, 4, 3, 3, 6

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OFFSET

1,2

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 77.

LINKS

Table of n, a(n) for n=1..32.

Eric Weisstein's MathWorld, Madelung Constants

FORMULA

M_5 = 1/sqrt(Pi) integral_{0..infinity} ((sum_{k=-infinity..infinity} ((-1)^k exp(-k^2 t))^5 - 1)/sqrt(t) dt

EXAMPLE

-1.9093378156187685595201437984336...

MATHEMATICA

digits = 32; f[n_, x_] := 1/Sqrt[Pi*x]*(EllipticTheta[4, 0, Exp[-x]]^n - 1); M[5] = NIntegrate[f[5, x], {x, 0, Infinity}, WorkingPrecision -> digits + 5]; RealDigits[M[5], 10, digits] // First

CROSSREFS

Cf. A088537, A085469, A090734, A247040, A261805, A264157.

Sequence in context: A278144 A198220 A131566 * A160576 A104756 A154994

Adjacent sequences: A264153 A264154 A264155 * A264157 A264158 A264159

KEYWORD

nonn,cons,more

AUTHOR

Jean-François Alcover, Nov 06 2015

STATUS

approved