Journal article
Two classes of special functions using fourier transforms of some finite classes of classical orthogonal polynomials
Publication Details
Authors: | Koepf, W.; Masjed-Jamei, M. |
Publication year: | 2007 |
Journal: | Proceedings of the American Mathematical Society |
Pages range : | 3599-3606 |
Volume number: | 135 |
Start page: | 3599 |
End page: | 3606 |
ISSN: | 0002-9939 |
Abstract
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.
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.
