Properties of q-holonomic functions

Author: Koepf Wolfram  

Publisher: Taylor & Francis Ltd

ISSN: 1023-6198

Source: Journal of Difference Equations and Applications, Vol.13, Iss.7, 2007-07, pp. : 621-638

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Abstract

In a similar manner as in the papers by W. Koepf, D. Schmersau, Spaces of functions satisfying simple differential equations, Konrad-Zuse-Zentrum Berlin (ZIB), Technical Report TR 94-2 (1994) and Salvy, B., Zimmermann, P., GFUN: A package for the manipulation of generating and holonomic functions in one variable, ACM Transactions on Mathematical Software, (1994), pp. 163-177, where explicit algorithms for finding the differential equations satisfied by holonomic functions were given, in this paper we deal with the space of the q-holonomic functions which are the solutions of linear q-differential equations with polynomial coefficients. The sum, product and the composition with power functions of q-holonomic functions are also q-holonomic and the resulting q-differential equations can be computed algorithmically.