Calculation of the Taylor series expansion coefficients of the Jacobian elliptic function

Author:
Staffan Wrigge

Journal:
Math. Comp. **36** (1981), 555-564

MSC:
Primary 65D20; Secondary 33A25

MathSciNet review:
606513

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Abstract | References | Similar Articles | Additional Information

Abstract: The Taylor series expansion coefficients of the Jacobian elliptic function and its power 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.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1981-0606513-8

Keywords:
Special functions,
elliptic functions,
Legendre polynomials

Article copyright:
© Copyright 1981
American Mathematical Society