Ramanujan-type continuous measures for classicalq-polynomials
Copyright policy )Ramanujan-type continuous measures for classicalq-polynomials
The author shows that the Ramanujan-type measures for a family of classical \(q\)-orthogonal polynomials can be built systematically from simple cases of continuous \(q\)-Hermite and \(p\)-Hermite polynomials \((p=q^{-1})\) by using a known procedure of attaching generating functions to measures. As an application of this technique, the author evaluates Ramanujan-type integrals for certain \(q\)-polynomials for \(01\), as well as for the product of four particular nonterminating basic (or \(q\)-) hypergeometric functions \({}_2\Phi_1\).
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), \(p\)-Hermite polynomials, Ramanujan-type measures, Applications of basic hypergeometric functions, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), \(p\)-Hermite polynomials, Ramanujan-type measures, Applications of basic hypergeometric functions, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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