Contiguous relations and summation and transformation formulas for basic hypergeometric series

Feng Gao; Victor J. W. Guo

Contiguous relations and summation and transformation formulas for basic hypergeometric series

Combinatorics 2013-04-23 v1

Authors: Feng Gao , Victor J. W. Guo

Abstract

By using contiguous relations for basic hypergeometric series, we give simple proofs of Bailey's $_4\phi_3$ summation, Carlitz's $_5\phi_4$ summation, Sears' $_3\phi_2$ to $_5\phi_4$ transformation, Sears' ${}_4\phi_3$ transformations, Chen's bibasic summation, Gasper's split poised $_{10}\phi_9$ transformation, Chu's bibasic symmetric transformation. Along the same line, finite forms of Sylvester's identity, Jacobi's triple product identity, and Kang's identity are also obtained.

Keywords

hypergeometric functions exponential sums

Cite

@article{arxiv.1304.5830,
  title  = {Contiguous relations and summation and transformation formulas for basic hypergeometric series},
  author = {Feng Gao and Victor J. W. Guo},
  journal= {arXiv preprint arXiv:1304.5830},
  year   = {2013}
}

Comments

14 pages, to appear in Journal of Difference Equations and Applications

Contiguous relations and summation and transformation formulas for basic hypergeometric series

Abstract

Keywords

Cite

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