NEW EXTENDED SRIVASTAVA HYPERGEOMETRIC FUNCTIONS AND THEIR VARIOUS INTEGRAL REPRESENTATIONS
Turkish Journal of Inequalities, vol.10, no.1, pp.131-141, 2026 (Scopus)
- Publication Type: Article / Article
- Volume: 10 Issue: 1
- Publication Date: 2026
- Journal Name: Turkish Journal of Inequalities
- Journal Indexes: Scopus
- Page Numbers: pp.131-141
- Keywords: beta function with general kernel, Exton’s function, gamma function, Gauss hypergeometric function, integral representations, Srivastava hypergeometric functions
- Ataturk University Affiliated: No
Abstract
This paper introduces novel and comprehensive extensions of the classical Srivastava hypergeometric functions HA, HB, and HC by incorporating a beta function with a general kernel into their definitions. Through this generalization, a broader class of hypergeometric-type functions is constructed, unifying several well-known special functions under a single analytical framework. In addition, various integral representations associated with these newly defined functions are systematically derived, providing deeper insights into their structural and operational properties. The proposed extensions not only enrich and generalize the theoretical foundation of classical hypergeometric functions but also significantly expand their applicability in diverse fields of mathematical analysis, fractional calculus, and applied sciences. These results are expected to open new avenues for further analytical investigation and for the modeling of complex phenomena arising in mathematical physics, engineering, and related disciplines.