Work

A sampling theorem of hypergeometric $$ _1F_2$$ functions and the Laguerre-Pólya class

Year: 2025

Type: article

Abstract: We investigate the pattern and the range of parameters for which hypergeometric $$ _1F_2$$ functions belong to the Laguerre-Pólya class with infinitely many real zeros. Our approach is based on the sampling theorem which provides sufficient conditions in terms of the sign of samples. In the case where the Lommel function comes into play, we use the differential equation method to determine the sign change, thereby specifying those parameters. As for the reality of all zeros of the Lommel function, our results give an extensive range of parameters, which turns out to be the best possible for the Struve function.

Source: Numerical Algorithms

DOI: 10.1007/s11075-025-02158-x

Authors: Yong-Kum Cho, Seok-Young Chung, Young Woong Park

Institutions: Chung-Ang University, University of Central Florida

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: National Research Foundation, Chung-Ang University, National Research Foundation of Korea, Ministry of Science and ICT, South Korea