## A new method and its Application to Generalized q-Bessel Polynomials (2001)

Venue: | Department of Mathematics, Uppsala University |

Citations: | 1 - 1 self |

### BibTeX

@TECHREPORT{Ernst01anew,

author = {Thomas Ernst},

title = {A new method and its Application to Generalized q-Bessel Polynomials},

institution = {Department of Mathematics, Uppsala University},

year = {2001}

}

### OpenURL

### Abstract

Abstract. We make a brief survey of orthogonal polynomials which are not included in the Askey scheme and we discuss some of their q-analogues. We reintroduce a notation of Heine, which leads to a new method for computations and classifications of q-special functions. As an example of this method, we present Bailey’s 1929 transformation formula for a terminating, balanced, verywell-poised 10φ9 q-hypergeometric series in the new notation. This series can occur in the Poisson kernel for the Askey-Wilson polynomials. We shall conclude by proving a new operator expression for q-Bessel polynomials and define new associated generalized q-Bessel polynomials, which will be used to find q-analogues of equations of Chatterjea and Srivastava. Contents