## Abstract

The q-Hermite polynomials are defined as a q-analogue of the matching polynomial of a complete graph. This allows a combinatorial evaluation of the integral used to prove the orthogonality of Askey and Wilson's _{4}φ_{3} polynomials. A special case of this result gives the linearization formula for q-Hermite polynomials. The moments and associated continued fraction are explicitly given. Another set of polynomials, closely related to the q-Hermite, is defined. These polynomials have a combinatorial interpretation in terms of finite vector spaces which give another proof of the linearization formula and the q-analogue of Mehler's formula.

Original language | English (US) |
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Pages (from-to) | 379-392 |

Number of pages | 14 |

Journal | European Journal of Combinatorics |

Volume | 8 |

Issue number | 4 |

DOIs | |

State | Published - 1987 |