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A264156 Decimal expansion of M_5, the 5-dimensional analog of Madelung's constant (negated). 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Nov 06 2015

STATUS

approved

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Last modified January 24 22:09 EST 2021. Contains 340414 sequences. (Running on oeis4.)