The Plancherel--Rotach Formula for Chebyshev--Hermite Functions on Half-Intervals Contracting to Infinity期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Larionchikov R S

Institution:	(1) Moscow Technical University of Communications and Information Science, Russia

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.

Keywords:	orthogonal polynomials Plancherel--Rotach asymptotic formula Chebyshev--Hermite functions Stirling formula
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