Product and Addition Formulas for the Continuous q-Ultraspherical Polynomials
Copyright policy )Product and Addition Formulas for the Continuous q-Ultraspherical Polynomials
Using Askey and Wilson's orthogonality relation and Rahman's product formula for Askey-Wilson polynomials a Gegenbauer-type product formula is obtained for continuous q-ultraspherical polynomials. Summation and transformation formulas for balanced hypergeometric series are then employed to derive a q-analogue of Gegenbauer's addition formula.
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), q-Saalschütz formula, Classical hypergeometric functions, \({}_2F_1\), Bailey's transformation formulas, Askey-Wilson polynomials, product formula, q-ultraspherical polynomials, balanced hypergeometric series
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), q-Saalschütz formula, Classical hypergeometric functions, \({}_2F_1\), Bailey's transformation formulas, Askey-Wilson polynomials, product formula, q-ultraspherical polynomials, balanced hypergeometric series
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