Generalized q-Laguerre type polynomials and q-partial differential equations
Keyword(s):
In this paper we define the q-Laguerre type polynomials Un(x; y; z; q), which include q-Laguerre polynomials, generalized Stieltjes-Wigert polynomials, little q-Laguerre polynomials and q-Hermite polynomials as special cases. We also establish a generalized q-differential operator, with which we build the relations between analytic functions and Un(x; y; z; q) by using certain q-partial differential equations. Therefore, the corresponding conclusions about q-Laguerre polynomials, little q-Laguerre polynomials and q-Hermite polynomials are gained as corollaries. As applications, some generating functions and generalized Andrews-Askey integral formulas are given in the final section.
2021 ◽
Vol 13
(2)
◽
pp. 413-426
1987 ◽
Vol 10
(1)
◽
pp. 163-172
2005 ◽
Vol 2005
(2)
◽
pp. 167-173
◽
2010 ◽
Vol 10
(03)
◽
pp. 341-366
◽
2017 ◽
Vol 454
(1)
◽
pp. 1-17
◽