This article is cited in 7 papers

Modified $q$-Bessel functions and $q$-Macdonald functions

M. A. Olshanetsky^a, V.-B. K. Rogov<sup>b

a</sup> Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
^b Moscow State University of Railway Communications

Abstract: The $q$-analogues of modified Bessel functions and Macdonald functions are defined in this paper. As in the case of $q$-Bessel functions introduced by Jackson, there are two kinds of these functions. Like their classical prototypes, they arise in harmonic analysis on quantum symmetric spaces. The definition is based on the power series expansion. Recurrence relations, difference equations, and $q$-Wronskians are obtained, as well as analogues of asymptotic expansions, which are convergent series if $q\ne 1$. Some relations for basic hypergeometric series, which result from this, are given.

UDC: 517.58

MSC: Primary 33C10; Secondary 33Dxx

Received: 23.01.1996

DOI: 10.4213/sm167

 English version: Sbornik: Mathematics, 1996, 187:10, 1525–1544

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