# Some Results Associated With K-Hypergeometric Functions

**Year of Publication:**2015

Vinita Gupta and Mukul Bhatt. Article: Some Results Associated With K-Hypergeometric Functions.

*IJAIS Proceedings on International Conference and Workshop on Communication, Computing and Virtualization*ICWCCV 2015(3):29-31, September 2015. BibTeX@article{key:article, author = "Vinita Gupta and Mukul Bhatt", title = "Article: Some Results Associated With K-Hypergeometric Functions", journal = "IJAIS Proceedings on International Conference and Workshop on Communication, Computing and Virtualization", year = 2015, volume = "ICWCCV 2015", number = 3, pages = "29-31", month = "September", note = "Published by Foundation of Computer Science, New York, USA" }

### Abstract

An integral representation of some generalized k-hypergeometric functions (introduced by Mubeen and Habibullah) is used to develop some new results of k-hypergeometric functions assuming different values of m in generalized k-hypergeometric functions. k-beta transform of k-hypergeometric functions is also obtained by using k-beta functions introduced by Diaz et al.

### Reference

- K. A. Driver and S. J. Johnston (2006), An integral representation of some hypergeometric functions, Electronic Transactions on Numerical Analysis, 25, 115-120.
- R. Diaz, and E. Pariguan (2007), On hypergeometric functions and Pochhammer k-symbol, Divulgaciones Matemticas, 15, 179-192.
- R. Diaz, and C. Teruel (2005), q; k-Generalized gamma and beta functions, Journal of Nonlinear Mathematical Physics, 12, 118-134.
- R. Diaz, C. Ortiz, and E. Pariguan (2010), On the kgamma qdistribution, Central European Journal of Mathematics, 8, 448-458.
- M. Mansour (2009), Determining the k-generalized gamma function by functional equations,Int. J. Contemp. Math. Sciences, 4, 1037-1042.
- C. G. Kokologiannaki (2010), Properties and inequalities of generalized k-gamma, beta and zeta functions, Int. J. Contemp. Math. Sciences, 5, 653-660.
- V. Krasniqi (2010), A limit for the k-gamma and k-beta function, Int. Math. Forum, 5, 1613-1617.
- V. Krasniqi (2010), Inequalities and monotonicity for the ration of k-gamma function, Scientia Magna, 6, 40-45.
- F. Merovci(2010), Power product inequalities for the
- k-gamma function, Int. J. Math. Analysis, 4, 1007-1012.
- S. Mubeen, and G. M. Habibullah (2012), An integral representation of some k-hypergeometric functions,
- International Mathematical Forum, 7, 203-207.
- S. Mubeen (2012), k-Analogue of Kummer's first formula, Journal of Inequalities and Special Functions, 3, 41-44.
- S. Mubeen (2013), Solution of Some Integral Equations Involving Confluent k-Hypergeometric Functions, Applied Mathematics, 4, 9-11.
- E. D. Rainville(1965), Special Functions, The Macmillan Company, New York.
- E. Pariguan, R. Diaz(2007), On hypergeometric functions and pochhammer k-symbol, Divulgaciones Matematicas,15,179-192.
- S. J. Lucy(1966), Generalized Hypergeometric Functions, Cambridge University Press.

### Keywords

k-gamma function, k-beta function, hypergeometric functions, generalized k-hypergeometric functions, k-beta transform