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Kibble–Slepian formula and generating functions for 2D polynomials |
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| Institution: | 1. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia;2. Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA;3. College of Science, Northwest A&F University, Yangling, Shaanxi 712100, PR China |
| Abstract: | We prove a generalization of the Kibble–Slepian formula (for Hermite polynomials) and its unitary analogue involving the 2D Hermite polynomials recently proved in 16]. We derive integral representations for the 2D Hermite polynomials which are of independent interest. Several new generating functions for 2D q-Hermite polynomials will also be given. |
| Keywords: | Hermite polynomials 2D Hermite polynomials Poisson kernels Positivity of kernels Integral operators Multilinear generating functions Kibble–Slepian formula |
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