Structural Properties and Integral Transforms of the k-Kummer Hypergeometric Function
Mathematics, cilt.14, sa.15, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 14 Sayı: 15
- Basım Tarihi: 2026
- Doi Numarası: 10.3390/math14152744
- Dergi Adı: Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: contiguous relations, generalized special functions, integral transforms, k-confluent hypergeometric function, k-Kummer function, operational identities
- Marmara Üniversitesi Adresli: Evet
Özet
In this paper, we study the k-Kummer hypergeometric function (Formula presented.), a generalization of the classical Kummer confluent hypergeometric function, arising as a solution of the k-confluent hypergeometric differential equation. We establish a Kummer-type transformation formula and derive derivative identities, contiguous relations, and addition and multiplication formulas. In addition, we obtain closed-form expressions for the Laplace, Mellin, Stieltjes, Sumudu, and Riemann–Liouville fractional integral transforms involving (Formula presented.). The results presented here extend the classical theory of confluent hypergeometric functions to the k-generalized setting and provide analytic tools for further investigations of generalized differential equations and integral transforms.