Generalization of Beta functions in terms of Mittag-Leffler function | ||||
Frontiers in Scientific Research and Technology | ||||
Article 10, Volume 1, Issue 1, 2020, Page 81-88 PDF (765.13 K) | ||||
Document Type: Original Article | ||||
DOI: 10.21608/fsrt.2020.39397.1023 | ||||
View on SCiNiTO | ||||
Authors | ||||
Karima M. Oraby 1; Ahmed Rizq2; Ehab Abdelhak2; Mostafa Taema3; Moamen Magdy2; Mohamed Khaled2 | ||||
1El-Salam | ||||
2Mathematics and Computer Science Department, Faculty of Science, Suez University | ||||
3Mathematics and Computer science Department , Faculty of Science, Suez University | ||||
Abstract | ||||
In this paper, we give a new generalization of extended beta functions by using generalized Mittag Leffler functions. We investigate its properties and its integral representations. In addition, we establish the generalization of extended hypergeometric and Confluent hypergeometric functions by using the newly extended beta function. Some properties of these extended and Confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are also investigated. In this paper, we give a new generalization of extended beta functions by using generalized Mittag Leffler functions. We investigate its properties and its integral representations. In addition, we establish the generalization of extended hypergeometric and Confluent hypergeometric functions by using the newly extended beta function. Some properties of these extended and Confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are also investigated. In this paper, we give a new generalization of extended beta functions by using generalized Mittag Leffler functions. We investigate its properties and its integral representations. In addition, we establish the generalization of extended hypergeometric and Confluent hypergeometric functions by using the newly extended beta function. Some properties of these extended and Confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are also investigated. | ||||
Keywords | ||||
Beta function; hypergeometric functions; Confluent hypergeometric functions | ||||
Statistics Article View: 307 PDF Download: 445 |
||||