Basic Hypergeometric Series

By Wenchang Chu, Di Claudio Leontina. 2004

618 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0cf27a5ce0624a70df0d438adda5e084c9e1652c

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Citations in the corpus

Applications of q-Taylor theorems (2003, unknown): “6) may be summed by the q-Gauss theorem [4] if β = a 2 to obtain a quadratic transformation (see [2] or (7.”
Galois theory of fuchsian $q$-difference equations (2002, unknown): “Whenq→ 1, q-analogs of special functions (like Heine’s basic hypergeometric series , see the “bible” [15]) “tend to” their classical counterpart.”
The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case (2006, background): “…polynomials 2000 Mathematics Subject Classification: 33D80; 33D45 Dedicated to the memory of Vadim Kuznetsov Briefly after I had moved from CWI, Amsterdam to a professorship at the University of Amsterdam in 1992, Vadim Kuznetsov contacted me about the possibility to come to Amsterdam as a postdoc.”
LEONARD PAIRS AND THE ASKEY-WILSON RELATIONS (2003, background): “The connection to polynomials is as follows: there is a natural correspondence between Leonard pairs and a class of orthogonal polynomials consisting of the qRacah polynomials [1, 5] and some related polynomials of the Askey-scheme [18, 36, 37].”
Enumeration of totally positive Grassmann cells (2003, background): “It is sufficient to show that the coefficient of [2]t1t2[3]t2t3 .”
Completely monotonic functions involving the gamma and q-gamma functions (2005, unknown): “The q-gamma function is, [13], Γq(z) := (1 − q)1−z ∞ ∏”
Elliptic hypergeometric series on root systems (2002, background): “In a wide sense, this field includes a large number of different extensions of Gauss’s hypergeometric series, such as the basic hypergeometric series or q-series first studied by Cauchy and Heine [GR].”
On integral representations of $q$-gamma and $q$-beta functions (2003, background): “Though the literature on the q–gamma function and its applications is rather extensive, [2], [3], [1], the authors usually avoided the use of its q–integral representation.”