𝑞-Tricomi functions and quantum algebra representations

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 (ω) () of the two-dimensional quantum algebra ℰ q ⁢ (2) Eₐ (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.