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Calculation of the Taylor series expansion coefficients of the Jacobian elliptic function ${\rm sn}(x,\,k)$
1981
Mathematics of Computation
The Taylor series expansion coefficients of the Jacobian elliptic function sn(x, k) and its power sn2(x, k) are studied. Recurrence formulae are given, and tables of the coefficients constructed. Using Lagrange's inversion formula, these coefficients can be expressed in terms of Legendre polynomials.
doi:10.1090/s0025-5718-1981-0606513-8
fatcat:qeqy7dmkwjgfpkam4dnh5nxzeu