Calculation of the Taylor series expansion coefficients of the Jacobian elliptic function ${\rm sn}(x,\,k)$

Staffan Wrigge
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