期刊
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
卷 135, 期 11, 页码 3599-3606出版社
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9939-07-08889-2
关键词
classical orthogonal polynomials; Fourier transform; hypergeometric functions; Gosper identity; Ramanujan integral
Some orthogonal polynomial systems are mapped onto each other by the Fourier transform. The best-known example of this type is the Hermite functions, i. e., the Hermite polynomials multiplied by exp(-x(2)/ 2), which are eigenfunctions of the Fourier transform. In this paper, we introduce two new examples of finite systems of this type and obtain their orthogonality relations. We also estimate a complicated integral and propose a conjecture for a further example of finite orthogonal sequences.
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