Generalizations of generating functions for basic hypergeometric orthogonal polynomials

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SUMMARY

Define ∞ ( a; q)∞:= ∏ (1 - aqn ), n=0 where 0 and amp;lt; |q| and amp;lt; 1, a ∈ C. Let n ∈ N0, α, β ∈ (-1, ∞), 0 and amp;lt; |q| and amp;lt; 1, |t| and amp;lt; (1 - qα+1 )(1 - q). Let n ∈ N0, α, β ∈ (-1, ∞), γ ∈ C, 0 and amp;lt; |q| and amp;lt; 1, |t| and amp;lt; 1 - q. Let n ∈ N0, 0 and amp;lt; |q| and amp;lt; 1, α, β ∈ (-1, ∞), |t| and amp;lt; (1 - qα+1 )(1 - q), c > 0. Let n ∈ N0, 0 and amp;lt; |q| and . . .

 



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