An Extended Wright Function

Abstract

In this paper we will extend the classical function Wright $W_{\alpha, \beta}(z)$ $\rightarrow$ $W_{\alpha, \beta}^{\lambda, \xi}(z)$ using the relationship between Euler beta function with the symbol Pochhammer $\frac{B(\lambda+n,\xi-\lambda)}{B(\lambda,\xi-\lambda)}=\frac{(\lambda)_{n}}{(\xi)_{n}}$. Some basic properties are studied and Laplace transform is evaluate \cite{1,3}. We will study the Riemann-Liouville fractional integral and fractional derivative arbitrary order $v$ of $W_{\alpha, \beta}^{\lambda, \xi}(z)$.