The new Mittag-Leffler function and its applications (Q2228157)

Summary: In this paper, we investigate some properties of the Pochhammer \((p,s,k)\)-symbol \({}_p [\xi]_{n,k,s}\) and gamma \((p,s,k)\)-function \({}_p \Gamma_{s,k} (\xi)\). We then prove several identities for newly defined symbol \({}_p [\xi]_{n,k,s}\) and the function \({}_p \Gamma_{s,k} (\xi)\). The integral representations for the gamma \((p,s,k)\)-function and beta \((p,s,k)\)-function are presented. Also, we define a new Mittag-Leffler \((p,s,k)\)-function and study its analytic properties and its transforms.