The problem of Taylor's series is therefore to deduce from a knowledge of the coefficients the behaviour of the function.

The paper covers a variety of ways to calculate the function ranging from various Taylor series approximations, Lagrange interpolation, and Chebyshev interpolation.

Conjectures on the Taylor Series Expansion Coefficients of the Jacobian Elliptic Function $\mathrm {sn} (x, k)$, Mathematics of Computation, Vol. 37, No. 156 (Oct., 1981), pp. 475-494 ...