Power series for inverse Jacobian elliptic functions
نویسنده
چکیده
The 12 inverse Jacobian elliptic functions are expanded in power series by using properties of the symmetric elliptic integral of the first kind. Suitable notation allows three series to include all 12 cases, three of which have been given previously. All coefficients are polynomials in the modulus k that are homogeneous variants of Legendre polynomials. The four series in each of three subsets have the same coefficients in terms of k.
منابع مشابه
Inequalities for Jacobian elliptic functions and Gauss lemniscate functions
A new proof of inequalities involving Jacobian elliptic functions and their inverse functions are obtained. Similar results for the Gauss lemniscate functions are also established. Upper bounds for the inverse Jacobian elliptic functions and for the Gauss arc lemniscate functions are derived. 2012 Elsevier Inc. All rights reserved.
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عنوان ژورنال:
- Math. Comput.
دوره 77 شماره
صفحات -
تاریخ انتشار 2008