Analytic Continuation of Generalized Trigonometric Functions
Pisheng Ding
TL;DR
This paper introduces a geometric method to analytically extend generalized trigonometric functions with two parameters, exploring their univalence, convergence, and periodicity properties.
Contribution
It provides a unified geometric framework for extending these functions and analyzing their fundamental properties beyond their initial domains.
Findings
Determined maximal domains for univalence of generalized trigonometric functions
Established results on the radius of convergence for their Maclaurin series
Explored continuation beyond univalence domains and their periodicity
Abstract
Via a unified geometric approach, a class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some consequences are deduced concerning radius of convergence for the Maclaurin series, commutation with rotation, continuation beyond the domain of univalence, and periodicity.
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Taxonomy
TopicsIterative Methods for Nonlinear Equations · Mathematical functions and polynomials · Fractional Differential Equations Solutions