Some properties concerning the analysis of generalized Wright function (Q1987442)

The Bessel-Maitland function, also called the Wright generalized Bessel function, is defined by \(W_{\alpha ,\beta } (z)=\sum _{n=0}^{\infty }\frac{z^{n} }{n!\Gamma (\alpha n+\beta )} \quad (\beta \in \mathrm{C},\; Re\, \alpha >-1)\). Various generalizations exist, for example, \(W_{\alpha ,\beta }^{\gamma ,\delta } (z)=\sum _{n=0}^{\infty }\frac{z^{n} (\gamma )_{n} }{n!(\delta )_{n} \Gamma (\alpha n+\beta )} \quad \left((a)_{n} =\frac{\Gamma (a+n)}{\Gamma (a)} \right)\). In this paper the authors give a further generalization of this function and provide some properties and applications.