2014/06/06 by Ayumu Hoshino, Hoshino, A., Masatoshi Noumi +3
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1406.1628
openalex publication_date 2014/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a fourfold series expansion representing the Askey-Wilson polynomials. To obtain the result, a sequential use is made of several summation and transformation formulas for the basic hypergeometric series, including the Verma's q-extension of the Field and Wimp expansion, Andrews' terminating q-analogue of Watson's 3F2 sum, Singh's quadratic transformation. As an application, we present an explicit formula for the Koornwinder polynomial of type BCn (n in Z_>0) with one row diagram. When the parameters are specialized, we recover Lassalle's formula for Macdonald polynomials of type Bn, Cn and Dn with one row diagram, thereby proving his conjectures.