A new approach to hypergeometric functions via ad-time scale
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.55, no.4, pp.1540-1562, 2026 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 55 Issue: 4
- Publication Date: 2026
- Doi Number: 10.15672/hujms.1800859
- Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Page Numbers: pp.1540-1562
- Dokuz Eylül University Affiliated: Yes
Abstract
This manuscript investigates hypergeometric functions on a general discrete time scale T alpha. To this end, we introduce the cx-b eta function, establish its fundamental properties, and explore its connection with the cx-gamma function. In order to achieve our main objective, we formulate the cx-analogue of the hypergeometric equation and construct its solutions, referred as the cx-hypergeometric functions. In parallel with the classical case, we illustrate that the cx-hypergeometric function encompasses many cx-elementary functions. Furthermore, we derive several key properties of the cx-hypergeometric function, including the cx-analogues of the Gauss summation formula, Pfaff transformation, and Eulers linear identity, which reduce to their classical and q-analogous forms.