Partial Fraction Expansions and Zeros of Hankel Transforms
Abstract
It is proved by the method of partial fraction expansion and Sturm’s oscillation theory that the zeros of certain Hankel transforms are all real, simple and distributed one by one between consecutive zeros of Bessel functions. As an application, we obtain a list of sufficient conditions as well as necessary conditions on parameters for which $${}_1F_2$$ hypergeometric functions belong to the Laguerre-Pólya class.
Fields of Study & Subjects
Mathematical functions and polynomials
Mathematical Analysis and Transform Methods
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Constructive Approximation
- Publisher
- Springer Science and Business Media LLC
- Volume
- 63
- Issue
- 3
- Pages
- 855–892
- Publication date
- 19 February 2026
- Language
- EN