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

Author

Jean-François Alcover, Sep 10 2014

Keywords

• nonn
• cons
• easy

Examples

			-0.670908307882478806085271599253853426816260971797672535...
		

References

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

Links

• Eric Weisstein's World of Mathematics, Lattice Sum.

Crossrefs

Cf. A247042.

Programs

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

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

Formula

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