Integral Transforms for the New Generalized Beta Function

Year 2019, Issue: 28, 53 - 61, 07.05.2019

Ahmed Ali Al-gonah Waleed Khadher Mohammed

Abstract

In this paper, some representation formulas for the generalized Gamma and Beta functions are obtained. Also, certain integral transforms for the generalized Beta function associated with the Wright hypergeometric function are derived.

Keywords

Gamma function, Beta function, integral transform

References

• A. A. Al-Gonah, W.K. Mohammed, A new extension of extended Gamma and Beta functions and their properties, Journal of Scientific and Engineering Research, 5 (9) (2018), 257-270
• T.R. Prabhakar, A singular integral equation with a Generalized Mittag-Leffler Function in the Kernel}, Yokohama Mathematical Journal, 19 (1971), 7-15.
• E. Özergin, Some properties of hypergeometric functions}, PhD dissertation, Eastern Mediterranean University (2011), North Cyprus, Turkey.
• M. A. Chaudhry, A. Qadir, M. Rafique, S. M. Zubair, Extension of Euler's Beta Function, Journal of Computational and Applied Mathematics, 78 (1997), 19-32.
• M. A. Chaudhry, S. M. Zubair, \emph{Generalized incomplete gamma functions with applications}, Journal of Computational and Applied Mathematics, 55 (1994), 99-124.
• M. S. Shadab, S. J. Jabee, J. C. Choi, An extended Beta function and its applications, Far East Journal of Mathematical Sciences, 103 (2018), 235-251.
• P. I. Pucheta, A new extended beta function, International Journal of Mathematics And its Applications, 5 (3-c) (2017), 255-260.
• P. Agarwal, Certain properties of the generalized Gauss hypergeometric functions, Applied Mathematics and Information Sciences, 8 (5) (2014), 2315-2320.
• H. M. Srivastava, H. L. Manocha, A treatise on generating functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984.
• A. M. Mathai, R.K. Saxena, H.J. Haubold, The H-Function Theory and Applications, Springer-Verlag New York, 2010.
• A. K. Shukla, J. C. Prajapati, On a generalization of Mittag-Leffler function and its properties, Journal of Mathematical Analysis and Applications, 336 (2007), 797-811.
• I. N. Sneddon, The Use of Integral Transforms, Tata McGraw-Hill, New Delhi, India, 1979.
• A. Dixit, V. H. Moll, The integrals in Gradshteyn and Ryzhik. Part 28: The confluent hypergeometric function and Whittaker functions, Series A: Mathematical Sciences, 26 (2015), 49-61.