APPLICATIONS OF BASIC HYPERGEOMETRIC FUNCTIONS.

Research output: Contribution to journalArticle

151 Citations (Scopus)

Abstract

The application of basic hypergeometric functions to partitions is briefly discussed. It is shown how bilateral basic hypergeometric series have application in number theory (apart from partitions). The relationship between finite vector spaces and basic hypergeometric functions is discussed; the theory of Eulerian differential operators, which arose from the combinatorial theory of finite vector spaces, and which has interesting applications to basic hypergeometric series, is briefly described. Finally, the usefulness of both ordinary and basic hypergeometric functions in the proof of and classification of combinatorial identities, and some of the recent applications of basic hypergeometric functions in physics are discussed.

Original languageEnglish (US)
Pages (from-to)441-484
Number of pages44
JournalSIAM Review
Volume16
Issue number4
DOIs
StatePublished - Jan 1 1974

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Basic Hypergeometric Functions
Basic Hypergeometric Series
Vector spaces
Vector space
Partition
Number theory
Combinatorial Identities
Differential operator
Physics

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computational Mathematics
  • Applied Mathematics

Cite this

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APPLICATIONS OF BASIC HYPERGEOMETRIC FUNCTIONS. / Andrews, George E.

In: SIAM Review, Vol. 16, No. 4, 01.01.1974, p. 441-484.

Research output: Contribution to journalArticle

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