Generalized q-difference equations for (q, c)-hypergeometric polynomials and some applications
In this paper, our investigation is motivated by the concept of ( q , c )-derivative operators introduced by Zhang (Adv Appl Math 121:102081, 2020). Then we seek and find that ( q , c )-hypergeometric polynomials involving ( q , c )-derivative operators are solutions of certain generalized q -dif...
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| Published in: | The Ramanujan journal Vol. 60; no. 4; pp. 1033 - 1067 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
Springer US
01.04.2023
|
| Subjects: | |
| ISSN: | 1382-4090, 1572-9303 |
| Online Access: | Get full text |
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| Summary: | In this paper, our investigation is motivated by the concept of (
q
,
c
)-derivative operators introduced by Zhang (Adv Appl Math 121:102081, 2020). Then we seek and find that (
q
,
c
)-hypergeometric polynomials involving (
q
,
c
)-derivative operators are solutions of certain generalized
q
-difference equations. We introduce two homogeneous (
q
,
c
)-difference operators
T
c
(
a
,
b
,
d
,
u
,
v
,
x
D
c
,
y
)
and
E
c
(
a
,
b
,
d
,
u
,
v
,
x
θ
c
,
y
)
, which turn out to be suitable for studying two families of generalized (
q
,
c
)-Al-Salam–Carlitz polynomials
Φ
n
(
a
,
b
,
d
,
u
,
v
,
c
)
(
x
,
y
|
q
)
and
Υ
n
(
a
,
b
,
d
,
u
,
v
,
c
)
(
x
,
y
|
q
)
. Several
q
-identities such as: generating functions, Andrews–Askey integrals and
U
(
n
+
1
)
type
q
-binomial formulas for generalized
q
-polynomials are derived by the method of (
q
,
c
)-difference equations. |
|---|---|
| ISSN: | 1382-4090 1572-9303 |
| DOI: | 10.1007/s11139-022-00634-9 |