Result: A q-theorem of Pólya using Hurwitz partial fraction method: A \(q\)-theorem of Pólya using Hurwitz partial fraction method
Title:
A q-theorem of Pólya using Hurwitz partial fraction method: A \(q\)-theorem of Pólya using Hurwitz partial fraction method
Authors:
Source:
The Journal of Analysis. 33:369-385
Publisher Information:
Springer Science and Business Media LLC, 2024.
Publication Year:
2024
Subject Terms:
Pólya-Hurwitz partial fraction expansions, Representations of entire functions of one complex variable by series and integrals, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), \(q\)-sampling theory, Normal functions of one complex variable, normal families, zeros of entire functions
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
2367-2501
0971-3611
0971-3611
DOI:
10.1007/s41478-024-00839-9
Rights:
CC BY
Accession Number:
edsair.doi.dedup.....c3ac6d30b3c231ffa5f64f51253a0a4c
Database:
OpenAIRE
Further Information
We establish a q-counterpart of the method of partial fraction developed by Hurwitz-Pólya to investigate the zeros of q-cosine and q-sine transforms, where $$q \in (0,1)$$ q ∈ ( 0 , 1 ) is a fixed number. We prove reality and simplicity of the zeros and give a precise description of their distribution. The conditions imposed on both q and the integrand are less restrictive than previously assumed in the literature. A direct infinite partial fraction expansion is obtained via q-sampling theory.