Hybrid Algorithm via Reciprocal-Argument Transformation for Efficient Gauss Hypergeometric Evaluation in Wireless Networks

Jianping Cai and Zuobin Ying ()
Additional contact information
Jianping Cai: The Faculty of Data Science, City University of Macau, Macau 999078, China
Zuobin Ying: The Faculty of Data Science, City University of Macau, Macau 999078, China

Mathematics, 2025, vol. 13, issue 15, 1-18

Abstract: The rapid densification of wireless networks demands efficient evaluation of special functions underpinning system-level performance metrics. To facilitate research, we introduce a computational framework tailored for the zero-balanced Gauss hypergeometric function Ψ ( x , y ) ≜ F 1 2 ( 1 , x ; 1 + x ; − y ) , a fundamental mathematical kernel emerging in Signal-to-Interference-plus-Noise Ratio (SINR) coverage analysis of non-uniform cellular deployments. Specifically, we propose a novel Reciprocal-Argument Transformation Algorithm (RTA), derived rigorously from a Mellin–Barnes reciprocal-argument identity, achieving geometric convergence with O 1 / y . By integrating RTA with a Pfaff-series solver into a hybrid algorithm guided by a golden-ratio switching criterion, our approach ensures optimal efficiency and numerical stability. Comprehensive validation demonstrates that the hybrid algorithm reliably attains machine-precision accuracy ( ∼ 10 − 16 ) within 1 μs per evaluation, dramatically accelerating calculations in realistic scenarios from hours to fractions of a second. Consequently, our method significantly enhances the feasibility of tractable optimization in ultra-dense non-uniform cellular networks, bridging the computational gap in large-scale wireless performance modeling.

Keywords: Gauss hypergeometric functions; reciprocal-argument transformation; SINR coverage; golden-ratio threshold; pfaff transformation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/15/2354/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/15/2354/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:15:p:2354-:d:1708131

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().