On extended M-series

Dharmendra Kumar Singha,*

On extended M-series

Authors :

Dharmendra Kumar Singh^a,*

Author Address :

^aDepartment of Mathematics, University Institute of Engineering and Technology, Chhatrapati Shahu Ji Maharaj University, Kanpur (U.P.) India.

*Corresponding author.

Abstract :

This paper deals with extended M-series, which is extension of the generalized M-series [12]. Mittag-Leffler function, $\omega$-hypergeometric function, generalized $\omega$-
Gauss hypergeometric function, $\omega$-confluent hypergeometric function, Bessel-Maitland function can be deduced as special cases of our finding. Moreover, we obtain some theorem for extended M-series by using fractional calculus operators and many results associated with Riemann-Liouville, Weyl and Erdelyi-Kober operators. We begin our study from the following definitions.

Keywords :

Extended M-series, Saigo- Meada operators, Pathway fractional integral operator.

DOI :

Article Info :

Received : October 16, 2012; Accepted : January 17, 2013.