MODIFIED Q-BESSEL FUNCTIONS AND Q-MACDONALD FUNCTIONS

The q-analogues of modified Bessel functions and Macdonald functions a re defined in this paper. As in the case of q-Bessel functions introdu ced by Jackson, there are two kinds of these functions. Like their cla ssical prototypes, they arise in harmonic analysis on quantum symmetri c spaces. The definition is based on the power series expansion. Recur rence relations, difference equations, and q-Wronskians are obtained, as well as analogues of asymptotic expansions, which are convergent se ries if q not equal 1. Some relations for basic hypergeometric series, which result from this, are given.