Integral representations and zeros of the Lommel function and the hypergeometric ₁F₂ function

2023/12/01 by Federico Zullo, Zullo, Federico
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2312.00426

openalex publication_date 2023/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give different integral representations of the Lommel function s_μ,ν(z) involving trigonometric and hypergeometric ₂F₁ functions. By using classical results of Polya, we give the distribution of the zeros of s_μ,ν(z) for certain regions in the plane (μ,ν). Further, thanks to a well known relation between the functions s_μ,ν(z) and the hypergeometric ₁F₂ function, we describe the distribution of the zeros of ₁F₂ for specific values of its parameters.

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