On fractional $q$-extensions of some $q$-orthogonal polynomials

Published 18 Dec 2016 in math.CA | (1612.08597v1)

Abstract: Fractional $q$-extensions of some classical $q$-orthogonal polynomials are introduced and some of the main properties of the new defined functions are given. Next, a fractional $q$-difference equation of Gauss type is introduced and solved by means of power series method.

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