The k-Confluent Hypergeometric Function and its properties in Bicomplex Numbers
Kishka, Z., Saleem, M., Bakhet, A., Fathi, M. (2025). The k-Confluent Hypergeometric Function and its properties in Bicomplex Numbers. EKB Journal Management System, 10(1), 80-87. doi: 10.21608/sjsci.2025.340564.1238
Zenhom Kishka; Mohamed A. Saleem; Ahmed Bakhet; Mohamed Fathi. "The k-Confluent Hypergeometric Function and its properties in Bicomplex Numbers". EKB Journal Management System, 10, 1, 2025, 80-87. doi: 10.21608/sjsci.2025.340564.1238
Kishka, Z., Saleem, M., Bakhet, A., Fathi, M. (2025). 'The k-Confluent Hypergeometric Function and its properties in Bicomplex Numbers', EKB Journal Management System, 10(1), pp. 80-87. doi: 10.21608/sjsci.2025.340564.1238
Kishka, Z., Saleem, M., Bakhet, A., Fathi, M. The k-Confluent Hypergeometric Function and its properties in Bicomplex Numbers. EKB Journal Management System, 2025; 10(1): 80-87. doi: 10.21608/sjsci.2025.340564.1238

The k-Confluent Hypergeometric Function and its properties in Bicomplex Numbers

Sohag Journal of Sciences
Volume 10, Issue 1, March 2025, Page 80-87  XML PDF (198.16 K)
Document Type: Regular Articles
DOI: 10.21608/sjsci.2025.340564.1238
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Authors
Zenhom Kishka1; Mohamed A. Saleemorcid 1; Ahmed Bakhetorcid 2; Mohamed Fathi email orcid 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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