### 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 language | English (US) |
---|---|

Pages (from-to) | 441-484 |

Number of pages | 44 |

Journal | SIAM Review |

Volume | 16 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1974 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computational Mathematics
- Applied Mathematics

### Cite this

*SIAM Review*,

*16*(4), 441-484. https://doi.org/10.1137/1016081

}

*SIAM Review*, vol. 16, no. 4, pp. 441-484. https://doi.org/10.1137/1016081

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - APPLICATIONS OF BASIC HYPERGEOMETRIC FUNCTIONS.

AU - Andrews, George E.

PY - 1974/1/1

Y1 - 1974/1/1

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=0016115402&partnerID=8YFLogxK

U2 - 10.1137/1016081

DO - 10.1137/1016081

M3 - Article

AN - SCOPUS:0016115402

VL - 16

SP - 441

EP - 484

JO - SIAM Review

JF - SIAM Review

SN - 0036-1445

IS - 4

ER -