q-Difference equation and the Cauchy operator identities |
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Authors: | Da-qian Lu |
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Institution: | East China Normal University, Department of Mathematics, Shanghai 200241, PR China |
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Abstract: | In this paper, we verify the Cauchy operator identities by a new method. And by using the Cauchy operator identities, we obtain a generating function for Rogers-Szegö polynomials. Applying the technique of parameter augmentation to two multiple generalizations of q-Chu-Vandermonde summation theorem given by Milne, we also obtain two multiple generalizations of the Kalnins-Miller transformation. |
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Keywords: | q-Series Basic hypergeometric series q-Differential operator The Cauchy operator Multiple basic hypergeometric series |
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