Continued fractions and Bessel functions

2019/05/01 by Alina Al'bertovna Allahverdyan, Allahverdyan, Alina Al'bertovna
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #General Mathematics (math.GM) #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1905.02808

openalex publication_date 2019/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Elementary transformations of equations Aψ=λψ are considered. The invertibility condition (Theorem 1) is established and similar transformations of Riccati equations in the case of second order differential operator A are constructed (Theorem 2). Applications to continuous fractions for Bessel functions and Chebyshev polynomials are established. It is shown particularly that the elementary solutions of Bessel equations are related to a fixed point transformations of Riccati equations.

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