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The Plancherel--Rotach Formula for Chebyshev--Hermite Functions on Half-Intervals Contracting to Infinity

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Abstract

In this paper, we prove the Plancherel--Rotach asymptotic formula for the Chebyshev--Hermite functions \(( - 1)^n e^{x^2 /2} (e^{ - x^2 } )^{(n)} /\sqrt {2^n n!\sqrt \pi } \) and their derivatives for the case in which \( + \infty \) belongs to the domain of definition. A method for calculating the approximation accuracy is also given.

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Authors and Affiliations

  1. Moscow Technical University of Communications and Information Science, Russia

    R. S. Larionchikov

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  1. R. S. Larionchikov
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Larionchikov, R.S. The Plancherel--Rotach Formula for Chebyshev--Hermite Functions on Half-Intervals Contracting to Infinity. Mathematical Notes 72, 66–74 (2002). https://doi.org/10.1023/A:1019817121293

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  • DOI: https://doi.org/10.1023/A:1019817121293

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