Abstract
Using a set of transformations on a series-form product formula for the q-Wilson polynomials p n ( x; a, b, c, d; q) and the Nassrallah-Rahman integral representation of an 8 ϑ 7 series, a product formula in the integral form for the continuous q-Jacobi polynomials p n ( x; b, bq, − c, − cq; q 2) with a positive kernel is obtained in the case 0 ⩽ b < c < 1. The kernel is expressed as a sum of two nonterminating, very-well-poised, and balanced 10 ϑ 9 series. Some special and limiting cases are also discussed.
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