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Some Characterizations of the Extended Beta and Gamma Functions: Properties and Applications


Bachioua Lahcene*

Department of Basic Sciences, Prep. Year, P.O. Box 2440, University of Ha’il, Ha’il, Saudi Arabia. 

*Correspondence: drbachioua@gmail.com (Dr. Bachioua Lahcene, Associate Professor, Department of Basic Sciences, Prep. Year, P.O. Box 2440, University of Ha’il, Ha’il, Saudi Arabia).

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ABSTRACT

The article represents the elementary and general introduction of some characterizations of the extended gamma and beta Functions and their important properties with various representations. This paper provides reviews of some of the new proposals to extend the form of basic functions and some closed-form representation of more integral functions is described. Some of the relative behaviors of the extended function, the special cases resulting from them when fixing the parameters, the decomposition equation, the integrative representation of the proposed general formula, the correlations related to the proposed formula, the frequency relationships, and the differentiation equation for these basic functions were investigated. We also investigated the asymptotic behavior of some special cases, known formulas, the basic decomposition equation, integral representations, convolutions, recurrence relations, and differentiation formula for these target functions by studying. Applications of these functions have been presented in the evaluation of some reversible Laplace transforms to the complex of definite integrals and the infinite series of related basic functions. 

Keywords: Extended, Gamma, Incomplete gamma, Functions, Properties, Applications, and Transformation.

Citation: Lahcene B. (2021). Some characterizations of the extended beta and gamma functions: properties and applications, Int. J. Mat. Math. Sci., 3(5), 101-112. 

https://doi.org/10.34104/ijmms.021.01010112


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