On the unimodality of the Taylor expansion coefficients of Jacobian elliptic functions

2018/07/23 by Shi-Mei Ma, Ma, Shi-Mei, Jun Ma +5
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Nonlinear Waves and Solitons #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1807.08700

Abstract

The Jacobian elliptic functions are standard forms of elliptic functions, and they were independently introduced by C.G.J. Jacobi and N.H. Abel. In this paper, we study the unimodality of Taylor expansion coefficients of the Jacobian elliptic functions sn(u,k) and cn(u,k). By using the theory of gamma-positivity, we obtain that the Taylor expansion coefficients of sn(u,k) are symmetric and unimodal, and that of cn(u,k) are unimodal and alternatingly increasing.

Citations

• Gamma-positivity in combinatorics and geometry
• The on-line encyclopedia of integer sequences

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