A Review of q-Difference Equations for Al-Salam-Carlitz Polynomials and Applications to U(n+1) Type Generating Functions and Ramanujan's Integrals

被引：10
作者：
Cao, Jian [1 ]
Huang, Jin-Yan [1 ]
Fadel, Mohammed [2 ]
Arjika, Sama [3 ]
机构：
[1] Hangzhou Normal Univ, Sch Math, Hangzhou 311121, Peoples R China
[2] Aligarh Muslim Univ, Dept Math, Aligarh 202002, India
[3] Univ Agadez, Dept Math & Informat, Agadez 900288, Niger
来源：
MATHEMATICS | 2023年 / 11卷 / 07期
基金：
中国国家自然科学基金;
关键词：
q-difference equation; q-exponential operator; Al-Salam-Carlitz polynomials; generating functions; Ramanujan's integral; OPERATOR IDENTITIES; TRANSFORMATION; EXPANSIONS; EXTENSION; SUMMATION; SERIES; BETA;
D O I：
10.3390/math11071655
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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-Szego 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.
引用
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页数：22
相关论文
共 57 条
  • [21] Chen WYC., 1998, MATH ESSAYS HONOR GI, P111, DOI [10.1007/978-1-4612-4108-9_5, DOI 10.1007/978-1-4612-4108-9_5]
  • [22] Remarks on Homogeneous Al-Salam and Carlitz Polynomials
    Fang, Jian-Ping
    [J]. JOURNAL OF MATHEMATICS, 2014, 2014
  • [23] Remarks on a generalized q-difference equation
    Fang, Jian-Ping
    [J]. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2015, 21 (10) : 934 - 953
  • [24] q-Difference equation and q-polynomials
    Fang, Jian-Ping
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 248 : 550 - 561
  • [25] Gasper George, 2004, BASIC HYPERGEOMETRIC, V96, DOI 10.1017/CBO9780511526251
  • [26] Orthogonality relations for Al-Salam-Carlitz polynomials of type II
    Groenevelt, Wolter
    [J]. JOURNAL OF APPROXIMATION THEORY, 2015, 195 : 89 - 108
  • [27] Gunning R., 1990, FUNCTION THEORY, V1, P203
  • [28] Hetmaniok E, 2019, 2019 APPLICATIONS OF ELECTROMAGNETICS IN MODERN ENGINEERING AND MEDICINE (PTZE), P56, DOI 10.23919/PTZE.2019.8781732
  • [29] ON SIMILARITIES BETWEEN EXPONENTIAL POLYNOMIALS AND HERMITE POLYNOMIALS
    Hetmaniok, Edyta
    Pleszczynski, Mariusz
    Slota, Damian
    Witula, Roman
    [J]. JOURNAL OF APPLIED MATHEMATICS AND COMPUTATIONAL MECHANICS, 2013, 12 (03) : 93 - 104
  • [30] Iterated integrals of polynomials
    Hetmaniok, Edyta
    Lorenc, Piotr
    Pleszczynski, Mariusz
    Witula, Roman
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 249 : 389 - 398
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