The k-Confluent Hypergeometric Function and its properties in Bicomplex Numbers | ||
| Sohag Journal of Sciences | ||
| Volume 10, Issue 1, March 2025, Pages 80-87 PDF (198.16 K) | ||
| Document Type: Regular Articles | ||
| DOI: 10.21608/sjsci.2025.340564.1238 | ||
| Authors | ||
| Zenhom Kishka1; Mohamed A. Saleem1; Ahmed Bakhet2; Mohamed Fathi* 1 | ||
| 1Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt. | ||
| 2Department of Mathematics, Faculty of Science Al-Azhar University, Assiut 71524, Egypt | ||
| Abstract | ||
| In this paper, we examine a specialized form of the bicomplex hypergeometric function, known as the $k$-bicomplex confluent hypergeometric function (CHF). We introduce a detailed analysis of its properties, focusing on its formulation with bicomplex parameters, convergence conditions, and derivative and integral representations. By exploring the $k$-confluent case, we highlight unique theoretical insights and practical applications, particularly within the framework of bicomplex $k$-Riemann-Liouville (R-L) Fractional calculus. Our findings expand the current understanding of bicomplex functions in applied sciences and mathematical analysis, laying a foundation for further exploration in specialized functions and fractional operators within the bicomplex domain. In this paper, we examine a specialized form of the bicomplex hypergeometric function, known as the $k$-bicomplex confluent hypergeometric function (CHF). We introduce a detailed analysis of its properties, focusing on its formulation with bicomplex parameters, convergence conditions, and derivative and integral representations. By exploring the $k$-confluent case, we highlight unique theoretical insights and practical applications, particularly within the framework of bicomplex $k$-Riemann-Liouville (R-L) Fractional calculus. Our findings expand the current understanding of bicomplex functions in applied sciences and mathematical analysis, laying a foundation for further exploration in specialized functions and fractional operators within the bicomplex domain. | ||
| Keywords | ||
| Bicomplex gamma and beta functions; Bicomplex hypergeometric functions; Fractional calculus; Bicomplex fractional operators; k-Riemann-Liouville operator | ||
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