Uniform asymptotic behaviour of Jacobi-\sn near a singular point. The Lost formula from handbooks for elliptic functions

2015/10/22 by O. M. Kiselëv, Kiselev, Oleg
Mathematics · #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1510.06602

openalex publication_date 2015/10/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this work we construct uniform asymptotic expansion of \sn(t|m) - Jacobi when m→1-0. The constructed expansion is valid over more than a half of period. The turning point is included into the interval of validity for the approximation. In addition we obtain the asymptotic formula for elliptic integral of the first kind and discuss the differences with the same formula from a handbook.

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