𝑞-Tricomi functions and quantum algebra representations
Mumtaz Riyasat, Tabinda Nahid, Subuhi Khan
Abstract
Abstract The quantum groups nowadays attract a considerable interest of mathematicians and physicists. The theory of q -special functions has received a group-theoretic interpretation using the techniques of quantum groups and quantum algebras. This paper focuses on introducing the q -Tricomi functions and 2D q -Tricomi functions through the generating function and series expansion and for the first time establishing a connecting relation between the q -Tricomi and q -Bessel functions. The behavior of these functions is described through shapes, and the contrast between them is observed using mathematical software. Further, the problem of framing the q -Tricomi and 2D q -Tricomi functions in the context of the irreducible representation <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>ω</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> {(\omega)} of the two-dimensional quantum algebra <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi mathvariant="script">ℰ</m:mi> <m:mi>q</m:mi> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mn>2</m:mn> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {\mathcal{E}_{q}(2)} is addressed, and certain relations involving these functions are obtained. 2-Variable 1-parameter q -Tricomi functions and their relationship with the 2-variable 1-parameter q -Bessel functions are also explored.