## Abstract

Wiener used the Poisson kernel for the Hermite polynomials to deal with the classical Fourier transform. Askey, Atakishiyev and Suslov used this approach to obtain a q-Fourier transform by using the continuous q-Hermite polynomials. Rahman and Suslov extended this result by taking the Askey-Wilson polynomials, considered to be the most general continuous classical orthogonal polynomials. The theory of q-Fourier transformation is further extended here by considering a nonsymmetric version of the Poisson kernel with Askey-Wilson polynomials. This approach enables us to obtain some new results, for example, the complex and real orthogonalities of these kernels.

Original language | English (US) |
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Pages (from-to) | 25-55 |

Number of pages | 31 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 68 |

Issue number | 1-2 |

DOIs | |

State | Published - Apr 22 1996 |

Externally published | Yes |

## Keywords

- Al-Salam-Chihara polynomials
- Askey-Wilson polynomials
- Basic hypergeometric series
- Fourier transform
- Hermite polynomials
- Integral transforms
- Poisson kernels
- q-Fourier transform
- q-orthogonal polynomials

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics