4 papers
Some -transformation formulas and Rogers-Ramanujan type identities
Chang Xu, Dunkun Yang
In this paper, we explore the role that Liu's transformation formula can play in discovering Rogers-Ramanujan type identities. Specifically, we combine Liu's transformation formula…
Representing Carlitz formula with q-shift operator
Dunkun Yang
This paper presents a new formula for the q-shift operator, building on the techniques by Liu and Sears. This formula provides fresh proof of the Carlitz formula and extends it nat…
Two -operational equations and Hahn polynomials
Jing Gu, DunKun Yang, Qi Bao
Motivated by Liu's recent work in \cite{Liu2022}. We shall reveal the essential feature of Hahn polynomials by presenting two new -exponential operators. These lead us to use a…
Notes on -partial differential equations for -Laguerre polynomials and little -Jacobi polynomials
Qi Bao, DunKun Yang
We define two common -orthogonal polynomials: homogeneous -Laguerre polynomials and homogeneous little -Jacobi polynomials. They can be viewed separately as solutions to t…