Summation formula for generalized discrete $q$-Hermite II polynomials
Summation formula for generalized discrete $q$-Hermite II polynomials
In this paper, we provide a family of generalized discrete $q$-Hermite II polynomials denoted by $\tilde{h}_{n,��}(x,y|q)$. An explicit relations connecting them with the $q$-Laguerre and Stieltjes-Wigert polynomials are obtained. Summation formula is derived by using different analytical means on their generating functions.
12 pages
Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable, FOS: Physical sciences, Mathematical Physics (math-ph), Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), connection formula, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, discrete \(q\)-Hermite II polynomials, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 33C45, 33D15, 33D50, basic orthogonal polynomials, Mathematical Physics
Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable, FOS: Physical sciences, Mathematical Physics (math-ph), Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), connection formula, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, discrete \(q\)-Hermite II polynomials, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 33C45, 33D15, 33D50, basic orthogonal polynomials, Mathematical Physics
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