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A261805 Decimal expansion of M_8, the 8th Madelung constant (negated). 4
2, 0, 5, 2, 4, 6, 6, 8, 2, 7, 2, 6, 9, 2, 7, 1, 2, 2, 8, 1, 7, 6, 3, 3, 7, 7, 9, 9, 1, 7, 3, 3, 8, 3, 9, 9, 1, 7, 0, 8, 3, 7, 7, 5, 2, 9, 9, 6, 5, 5, 8, 2, 1, 9, 3, 2, 3, 7, 3, 2, 4, 5, 7, 7, 5, 3, 4, 9, 9, 4, 1, 3, 2, 8, 7, 5, 2, 7, 0, 6, 1, 4, 6, 9, 8, 5, 1, 9, 8, 8, 3, 9, 4, 1, 3, 1, 7, 5, 1, 0, 8, 8, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

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

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

Eric Weisstein's MathWorld, Madelung Constants

FORMULA

M_8 = (15/(4*Pi^3))*(8*sqrt(2) - 1)*zeta(1/2)*zeta(7/2).

EXAMPLE

-2.052466827269271228176337799173383991708377529965582...

MATHEMATICA

M8 = (15/(4*Pi^3))*(8*Sqrt[2] - 1)*Zeta[1/2]*Zeta[7/2]; RealDigits[M8, 10, 103] // First

PROG

(PARI) th4(x)=1+2*sumalt(n=1, (-1)^n*x^n^2)

intnum(x=0, [oo, 1], (th4(exp(-x))^8-1)/sqrt(Pi*x)) \\ Charles R Greathouse IV, Jun 06 2016

CROSSREFS

Cf. A059750, A088537, A085469, A090734, A247040, A261804.

Sequence in context: A066283 A240663 A267213 * A300703 A300706 A014842

Adjacent sequences:  A261802 A261803 A261804 * A261806 A261807 A261808

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Sep 01 2015

STATUS

approved

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Last modified July 14 16:21 EDT 2020. Contains 335729 sequences. (Running on oeis4.)