A247043 Decimal expansion of gamma_2, a lattice sum constant, analog of Euler's constant for two-dimensional lattices.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 80.

Links

Table of n, a(n) for n=0..102.

Eric Weisstein's World of Mathematics, Lattice Sum.

Formula

gamma_2 = (1/4)*(delta_2 + 2*log((sqrt(2) + 1)/(sqrt(2) - 1)) - 4*EulerGamma), where delta_2 is A247042.

Example

-0.670908307882478806085271599253853426816260971797672535...

Mathematica

delta2 = 2*Zeta[1/2]*(Zeta[1/2, 1/4] - Zeta[1/2, 3/4]); gamma2 = (1/4)*(delta2 + 2*Log[(Sqrt[2] + 1)/(Sqrt[2] - 1)] - 4*EulerGamma); RealDigits[gamma2, 10, 103] // First

Prog

(PARI) (2*zeta(1/2)*(zetahurwitz(1/2, 1/4)-zetahurwitz(1/2, 3/4)) + 2*log((sqrt(2) + 1)/(sqrt(2) - 1)))/4 - Euler \\ Charles R Greathouse IV, Jan 31 2018

Crossrefs

Cf. A247042.

Sequence in context: A010499 A218012 A195714 * A019734 A273633 A021153

Adjacent sequences: A247040 A247041 A247042 * A247044 A247045 A247046

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 10 2014

Status

approved