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- W1482293925 abstract "We first study four different types of q-Hermite polynomials hν,q(x), ψν,q(x), kν,q(x), fν,q(x) from the point of view of generating functions and operational formulas. Three of these q-Hermite polynomials are q-Appell polynomials, and the remaining one is a pseudo q-Appell polynomial. q-difference equations and q-hypergeometric expressions are found. In this paper, we only obtain Rodriguez formulas for two of the four polynomials, namely hν,q(x) and kν,q(x), and accordingly we can only find q-analogues of the so-called Nielsen’s formula for these two polynomials. Matrix forms for the polynomials expressed by q-Pascal matrices are considered. An orthogonality relation for kν,q(x) expressed as a q-integral is found. The two Cigler q-Laguerre polynomials are introduced and with the help of the relationship between hν,q(x) and the q-Laguerre polynomials, new generating functions for hν,q(x) are found. In the second part of the paper we study orthogonality relations for q-Jacobi-, q-Laguerreand q-Legendre polynomials. The proofs will all use q-integration by parts, a method equivalent to the previously used recurrence technique. The orthogonality relations are all of discrete type." @default.
- W1482293925 created "2016-06-24" @default.
- W1482293925 creator A5042509034 @default.
- W1482293925 date "2008-01-01" @default.
- W1482293925 modified "2023-09-27" @default.
- W1482293925 title "EXAMPLES OF q-ORTHOGONAL POLYNOMIALS" @default.
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