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A247040 Decimal expansion of M_6, the 6th Madelung constant. 7
1, 9, 6, 5, 5, 5, 7, 0, 3, 9, 0, 0, 9, 0, 7, 8, 2, 8, 1, 3, 1, 2, 3, 1, 3, 5, 5, 5, 7, 3, 5, 1, 8, 5, 3, 6, 7, 8, 6, 8, 9, 7, 6, 7, 2, 8, 4, 4, 6, 4, 6, 4, 5, 1, 1, 7, 0, 8, 5, 6, 5, 2, 8, 8, 7, 8, 1, 7, 9, 6, 4, 0, 1, 4, 3, 2, 5, 3, 5, 4, 5, 7, 6, 4, 9, 3, 1, 3, 4, 2, 6, 6, 6, 3, 6, 7, 2, 6, 7, 6, 4, 2, 9, 8 (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

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

Eric Weisstein's MathWorld, Dirichlet Beta Function

Eric Weisstein's MathWorld, Madelung Constants

FORMULA

M6 = (3/Pi^2)*(4*(sqrt(2)-1)*zeta(1/2)*beta(5/2) - (4*sqrt(2)-1)*zeta(5/2)*beta(1/2)), where beta is Dirichlet's "beta" function.

EXAMPLE

-1.9655570390090782813123135557351853678689767284464645117...

MATHEMATICA

beta[x_] := (Zeta[x, 1/4] - Zeta[x, 3/4])/4^x; M6 = (3/Pi^2)*(4*(Sqrt[2]-1)*Zeta[1/2]*beta[5/2] - (4*Sqrt[2]-1)*Zeta[5/2]*beta[1/2]); RealDigits[M6, 10, 104][[1]]

PROG

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

intnum(x=0, [oo, 1], (th4(exp(-x))^6-1)/sqrt(Pi*x)) \\ Charles R Greathouse IV, Jun 07 2016

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

intnum(x=0, [oo, 1], (th4(exp(-x))^6-1)/sqrt(Pi*x)) \\ Charles R Greathouse IV, Jun 06 2016

CROSSREFS

Cf. A059750, A088537, A085469, A090734.

Sequence in context: A200138 A196772 A225406 * A019942 A102047 A144665

Adjacent sequences:  A247037 A247038 A247039 * A247041 A247042 A247043

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Sep 10 2014

STATUS

approved

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Last modified July 15 20:00 EDT 2019. Contains 325056 sequences. (Running on oeis4.)