Partial fraction expansions and zeros of Hankel transforms

2023/11/07 by Cho, Yong-Kum, Chung, Seok-Young, Park, Young Woong
#30D10 #33C10 #34C10 #44A15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.04385

Abstract

It is proved by the method of partial fraction expansions and Sturm's oscillation theory that the zeros of certain Hankel transforms are all real and distributed regularly between consecutive zeros of Bessel functions. As an application, the sufficient or necessary conditions on parameters for which ₁F₂ hypergeometric functions belong to the Laguerre-Pólya class are investigated in a constructive manner.

Related

• On the Zeros of q-Hankel Transform by Using Pólya-Hurwitz Partial Fraction Method
• Exact expansions of Hankel transforms and related integrals
• On sequences with -1,0,1 Hankel transforms
• Ramanujan's Master Theorem and two formulas for zero-order Hankel transform
• The zeros of certain Fourier transforms:Improvements of Pólya's results