OFFSET
0,1
REFERENCES
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 391-406.
LINKS
G. A. Baker, Further application of the Padé approximant method to the Ising and Heisenberg models, Phys. Rev. 129 (1963) 99-102.
I. G. Enting, A, J. Guttmann and I. Jensen, Low-Temperature Series Expansions for the Spin-1 Ising Model, arXiv:hep-lat/9410005, 1994; J. Phys. A. 27 (1994) 6987-7006.
Steven R. Finch, Lenz-Ising Constants [broken link]
Steven R. Finch, Lenz-Ising Constants [From the Wayback Machine]
FORMULA
G.f.: ((u^4 + 30*u^2 + 1) * K(x) / Pi - (u+1)^4 * E(x) / Pi - 2*u*(u+1)^2) / (u^2 * (u^2-1)^2) = 4 * (f(u) * (f'(u)/u + f''(u)) - (f'(u))^2) / f(u)^2, where f(u) is the g.f. of A002890, K(x) and E(x) are the complete elliptic integrals, x = 4*(1-u)*sqrt(u)/(1+u)^2. - Andrey Zabolotskiy, Feb 15 2022
a(n) ~ 2 * (1 + sqrt(2))^(2*n+4) / (Pi*n). - Vaclav Kotesovec, Apr 28 2024
MATHEMATICA
CoefficientList[Series[1/(Pi*x^2*(-1 + x^2)^2) * (-2*Pi*x*(1 + x)^2 - (1 + x)^4 * EllipticE[16*(-1 + x)^2*x/(1 + x)^4] + (1 + 30*x^2 + x^4) * EllipticK[16*(-1 + x)^2*x/(1 + x)^4]), {x, 0, 25}], x] (* Vaclav Kotesovec, Apr 28 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(18) and beyond from Andrey Zabolotskiy, Feb 15 2022
STATUS
approved