Generalized q-Modified Laguerre Functions

Abstract

In this paper we define a new q-special function A ^α _n (x, b, c; q). The new function is a generalization of the q-Laguerre function and the Stieltjes–Wigert function. We deduced all the properties of the function A _n ^α(x, b, c; q). Finally, lim _q→1 A _n ^α((1 − q)x, −β, 1;q) gives L _n ^(α,β)(x,q), which is a β-modification of the ordinary Laguerre function.