A recurring q -integral formula

• Published in: Applied mathematics letters Vol. 23; no. 3; pp. 256 - 260
• Main Author: Wang, Mingjin
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.03.2010; Elsevier
• Subjects: Aluminum; Exact sciences and technology; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Representations; Sciences and techniques of general use; Special functions; Stopping; The [formula omitted] basic hypergeometric series; The [formula omitted]-Chu–Vandermonde formula; The Al-Salam–Carlitz polynomials; The Andrews–Askey integral; The recurring [formula omitted]-integral formula; The terminating Sears’ [formula omitted] transformation formula; Transformations; The Al-Salam–Carlitz polynomials; The r + 1 ϕ r basic hypergeometric series; The recurring q -integral formula; The Andrews–Askey integral; The terminating Sears’ 3 ϕ 2 transformation formula; The q -Chu–Vandermonde formula; Polynomial; transformation formula; The Andrews-Askey integral; The Al-Salam-Carlitz polynomials; Applied mathematics; The r+1 φ; φ; The q-Chu-Vandermonde formula; basic hypergeometric series; The recurring q-integral formula; The terminating Sears
• ISSN: 0893-9659; 1873-5452
• DOI: 10.1016/j.aml.2009.10.004

In this paper, we use the q -Chu–Vandermonde formula to derive a recurring q -integral formula. Some applications of the recurring q -integral formula are also given, which include deriving the 3 ϕ 2 representation of the Al-Salam–Carlitz polynomials and the extension of the terminating Sears’ 3 ϕ 2 transformation formula.