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


Author: Staffan Wrigge
Journal: Math. Comp. 36 (1981), 555-564
MSC: Primary 65D20; Secondary 33A25
DOI: https://doi.org/10.1090/S0025-5718-1981-0606513-8
MathSciNet review: 606513
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Abstract | References | Similar Articles | Additional Information

Abstract: The Taylor series expansion coefficients of the Jacobian elliptic function $ {\text{sn}}(x,k)$ and its power $ {\text{sn}}^2(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.


References [Enhancements On Off] (What's this?)

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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

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