A q-summation formula,the continuous q-Hahn polynomials and the big q-Jacobi polynomials |
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Authors: | Zhi-Guo Liu |
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Affiliation: | Department of Mathematics, East China Normal University, 500 Dongchuan Road, Shanghai 200241, PR China |
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Abstract: | Using a general q-summation formula, we derive a generating function for the q-Hahn polynomials, which is used to give a complete proof of the orthogonality relation for the continuous q-Hahn polynomials. A new proof of the orthogonality relation for the big q-Jacobi polynomials is also given. A simple evaluation of the Nassrallah–Rahman integral is derived by using this summation formula. A new q-beta integral formula is established, which includes the Nassrallah–Rahman integral as a special case. The q-summation formula also allows us to recover several strange q-series identities. |
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Keywords: | q-series q-summation q-Hahn polynomials q-Jacobi polynomials Nassrallah&ndash Rahman integral |
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