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A029872
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Low temperature series for spin-1/2 Ising specific heat on 2D square lattice.
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4
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16, 72, 288, 1200, 5376, 25480, 125504, 634608, 3269680, 17086168, 90282240, 481347152, 2585485504, 13974825960, 75941188736, 414593263952, 2272626444528, 12502223573304, 68996534259040, 381858968527680, 2118806030647328, 11783826597027256, 65674579024955904
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OFFSET
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0,1
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 391-406.
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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