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

preprint2016arXivOpen access

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

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On fractional qqq-extensions of some qqq-orthogonal polynomials

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