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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
MathSciNet review: 606513
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1981-0606513-8
PII: S 0025-5718(1981)0606513-8
Keywords: Special functions, elliptic functions, Legendre polynomials
Article copyright: © Copyright 1981 American Mathematical Society