A STUDY OF THE EXTENDED τ, β -GAUSS HYPERGEOMETRIC FUNCTION

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Published: 2017-08-26

Page: 139-147


BHUPENDER SINGH SHAKTAWAT *

Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur – 342005, India

DEVENDRA SINGH RAWAT

Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur – 342005, India

RAJEEV KUMAR GUPTA

Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur – 342005, India

*Author to whom correspondence should be addressed.


Abstract

This paper deals with the study of a new generalization of Gauss hypergeometric function. We define here an extended τ, β-Gausshypergeometric function and various properties of this new function are investigated such as its integral representation, derivative formulas and Mellin transform. Fractional calculus approach of are also established. The results presented in this paper are of general nature and results given earlier by Parmar [1], Srivastava et al. [2], Virchenko and Rumiantseva [3] and Virchenko et al. [4] follows, as special cases.

Keywords: Generalized Pochhammer symbol, Gauss hypergeometric function, τ-Gauss hypergeometric function, Mellin transform and Fractional calculus


How to Cite

SHAKTAWAT, B. S., RAWAT, D. S., & GUPTA, R. K. (2017). A STUDY OF THE EXTENDED τ, β -GAUSS HYPERGEOMETRIC FUNCTION. Asian Journal of Mathematics and Computer Research, 19(3), 139–147. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/901

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