# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Balanced ${}_{3}{\phi }_{2}$ summation theorems for $U\left(n\right)$ basic hypergeometric series. (English) Zbl 0886.33014
The Bailey transform is G. E. Andrews’ [Proc. Symp. Pure Math. Am. Math. Soc., Columbus, Ohio 1978, Proc. Symp. Pure Math. 34, 1-24 (1979; Zbl 0403.33002)] codification in terms of matrix inversions of a technique of W. N. Bailey for generating new Rogers-Ramanujan type identities. It can also be used to exhibit the equivalence of certain pairs of identities such as the summation formulæ for the terminating balanced ${}_{3}{\phi }_{2}$ and the very-well-poised ${}_{6}{\phi }_{5}$. In this paper, the author moves all of this machinery up to the context of multiple basic hypergeometric series very-well-poised on $U\left(n+1\right)$. It is then used to recreate much of the classical theory of basic hypergeometric series in the more general context of multiple series over $U\left(n+1\right)$.