Oraby, K., Rizq, A., Abdelhak, E., Taema, M., Magdy, M., Khaled, M. (2020). Generalization of Beta functions in terms of Mittag-Leffler function. test, 1(1), 81-88. doi: 10.21608/fsrt.2020.39397.1023
Karima M. Oraby; Ahmed Rizq; Ehab Abdelhak; Mostafa Taema; Moamen Magdy; Mohamed Khaled. "Generalization of Beta functions in terms of Mittag-Leffler function". test, 1, 1, 2020, 81-88. doi: 10.21608/fsrt.2020.39397.1023
Oraby, K., Rizq, A., Abdelhak, E., Taema, M., Magdy, M., Khaled, M. (2020). 'Generalization of Beta functions in terms of Mittag-Leffler function', test, 1(1), pp. 81-88. doi: 10.21608/fsrt.2020.39397.1023
Oraby, K., Rizq, A., Abdelhak, E., Taema, M., Magdy, M., Khaled, M. Generalization of Beta functions in terms of Mittag-Leffler function. test, 2020; 1(1): 81-88. doi: 10.21608/fsrt.2020.39397.1023

Generalization of Beta functions in terms of Mittag-Leffler function

Frontiers in Scientific Research and Technology
Article 10, Volume 1, Issue 1, 2020, Pages 81-88    PDF (765.13 K)
Document Type: Original Article
DOI: 10.21608/fsrt.2020.39397.1023
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
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