Non linear difference equations arising from a deformation of the q-Laguerre weight
Abstract
We study, in this paper, a one parameter deformation of the q-Laguerre weight function. An investigation is made on the polynomials orthogonal with respect to such a weight. With the aid of the two compatibility conditions previously obtained in Chen-Ism and the q-analog of a sum rule obtained in this paper, we derive expressions for the recurrence coefficients in terms of certain auxiliary quantities, and show that these quantities satisfy a pair of first order non linear difference equations. These difference equations are similar in form to the recognized asymmetric discrete Painleve systems such as α q-P-IV and α q-P-V.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.