Keywords:-

Keywords: Beta function, Integral representations.

Article Content:-

Abstract

The main of this research is to provide a systematic review of a new type of generalized beta function beta function involving a new generalized hypergeometric function. We also obtain a certain integral representation and summation formulas. Furthermore, we also study beta distributions and their properties.

References:-

References

P. Agarwal, J. Choi, and R. B. Paris, “Extended Riemann-Liouville fractional derivative operator and its applications,” The Journal of Nonlinear Science and Applications, vol. 8, no. 5, pp. 451–466, 2015.

M. A. Chaudhary and S. M. Zubair, “Generalized incomplete gamma function with applications,” Journal of Computational and Applied Mathematics, vol. 55, no. 1, pp. 99–123, 1994.

M. A. Chaudhary, A. Qadir, H. M. Srivastava, and R. B. Paris, “Extended hypergeometric and confluent hypergeometric function,” Applied Mathematics and Computation, vol. 159, no. 2, pp. 589–602, 2004.

J. Choi, M. I. Qureshi, A. H. Bhat, and J. Majid, “Reduction formulas for generalized hypergeometric series associated with new sequences and applications,” Fractal Fract, vol. 5, p. 150, 2021.

J. Choi, “Certain applications of generalized Kummer’s summation formulas for 2F1,” Symmetry, vol. 13, p. 1538, 2021.

H. M. Srivastava and J. Choi, Zeta and Q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, New York, NY, USA, 2012.

H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press, New York, NY, USA, 1985.

M. A. Chaudhary, A. Qadir, M. Rafique, and S. M. Zubair, “Extension of Euler’s beta function,” Journal of Computational and Applied Mathematics, vol. 78, no. 1, pp. 19–32, 1997.

E. Ozergin, Some properties of hypergeometric functions, Ph.D. thesis, Eastern Mediterranean University, North Cyprus, Turkey, 2011.

E. Ozergin, M.A. Ozarslan, A. Altin, Extension of gamma ,beta and hypergeometric functions, J. Comput. Appl. Math., 235(2011), 4601-4610.

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

Downloads

Citation Tools

How to Cite
Dudi, N., Gurjar, M. K., & Vishnoi, A. K. (2023). Generalized Beta Functions Involving New Generalized Hypergeometric Functions and Its Applications. International Journal Of Mathematics And Computer Research, 11(8), 3627-3631. https://doi.org/10.47191/ijmcr/v11i8.01