Communications of the
Korean Mathematical Society CKMS

In this present paper, our aim is to introduce an extended Wright-Bessel function $J_{\alpha,q}^{\lambda,\gamma, c}(z)$ which is established with the help of the extended beta function. Also, we investigate certain integral transforms and generalized integration formulas for the newly defined extended Wright-Bessel function $J_{\alpha,q}^{\lambda,\gamma, c}(z)$ and the obtained results are expressed in terms of Fox-Wright function. Some interesting special cases involving an extended Mittag-Leffler functions are deduced.

Keywords: gamma function, generalized hypergeometric function, Oberhettinger formula, Wright-Bessel function, generalized Wright function, Mittag-Leffler function

MSC numbers: 33B20, 33C20, 33C45, 33C60, 33B15, 26A33