### Abstract

We introduce a double sum extension of a very well-poised series and extend to this the transformations of Bailey and Sears as well as the _{6}φ_{5} summation formula of F. H. Jackson and the q-Dixon sum. We also give q-integral representations of the double sum. Generalizations of the Nassrallah-Rahman integral are also found.

Original language | English (US) |
---|---|

Pages (from-to) | 543-567 |

Number of pages | 25 |

Journal | Canadian Journal of Mathematics |

Volume | 49 |

Issue number | 3 |

State | Published - Jun 1997 |

Externally published | Yes |

### Fingerprint

### Keywords

- Al-Salam-Chihara polynomials
- Balanced series
- Basic hypergeomctric series
- Integral representations
- Very well-poised series

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Canadian Journal of Mathematics*,

*49*(3), 543-567.

**Some summation theorems and transformations for q-series.** / Ismail, Mourad E H; Rahman, Mizan; Suslov, Sergei.

Research output: Contribution to journal › Article

*Canadian Journal of Mathematics*, vol. 49, no. 3, pp. 543-567.

}

TY - JOUR

T1 - Some summation theorems and transformations for q-series

AU - Ismail, Mourad E H

AU - Rahman, Mizan

AU - Suslov, Sergei

PY - 1997/6

Y1 - 1997/6

N2 - We introduce a double sum extension of a very well-poised series and extend to this the transformations of Bailey and Sears as well as the 6φ5 summation formula of F. H. Jackson and the q-Dixon sum. We also give q-integral representations of the double sum. Generalizations of the Nassrallah-Rahman integral are also found.

AB - We introduce a double sum extension of a very well-poised series and extend to this the transformations of Bailey and Sears as well as the 6φ5 summation formula of F. H. Jackson and the q-Dixon sum. We also give q-integral representations of the double sum. Generalizations of the Nassrallah-Rahman integral are also found.

KW - Al-Salam-Chihara polynomials

KW - Balanced series

KW - Basic hypergeomctric series

KW - Integral representations

KW - Very well-poised series

UR - http://www.scopus.com/inward/record.url?scp=0031490225&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031490225&partnerID=8YFLogxK

M3 - Article

VL - 49

SP - 543

EP - 567

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

SN - 0008-414X

IS - 3

ER -