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A Review of q -Difference Equations for Al-Salam–Carlitz Polynomials and Applications to U (n + 1) Type Generating Functions and Ramanujan's Integrals.
- Source :
-
Mathematics (2227-7390) . Apr2023, Vol. 11 Issue 7, p1655. 22p. - Publication Year :
- 2023
-
Abstract
- In this review paper, our aim is to study the current research progress of q-difference equations for generalized Al-Salam–Carlitz polynomials related to theta functions and to give an extension of q-difference equations for q-exponential operators and q-difference equations for Rogers–Szegö polynomials. Then, we continue to generalize certain generating functions for Al-Salam–Carlitz polynomials via q-difference equations. We provide a proof of Rogers formula for general Al-Salam–Carlitz polynomials and obtain transformational identities using q-difference equations. In addition, we gain U (n + 1) -type generating functions and Ramanujan's integrals involving general Al-Salam–Carlitz polynomials via q-difference equations. Finally, we derive two extensions of the Andrews–Askey integral via q-difference equations. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GENERATING functions
*POLYNOMIALS
*EQUATIONS
*OPERATOR equations
*INTEGRALS
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 11
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 163043005
- Full Text :
- https://doi.org/10.3390/math11071655