Journal article
Properties of q-holonomic functions
Publication Details
Authors: | Koepf, W.; Rajkovic, P.; Marinkovic, S. |
Publication year: | 2007 |
Journal: | Journal of Difference Equations and Applications |
Pages range : | 621-638 |
Volume number: | 13 |
Start page: | 621 |
End page: | 638 |
ISSN: | 1023-6198 |
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.
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.
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