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A general Heine transformation and symmetric polynomials of Rogers

  • Douglas Bowman
Part of the Progress in Mathematics book series (PM, volume 138)

Abstract

Our purpose here is first to give a multivariate generalization of the important transformation of Heine [6, pp. 305–306] (see also [1, ch.2]),
$$\begin{array}{*{20}c} {2^\Phi 1\,\left( {{}_c^{a,\,b} ;\,z} \right)\, = \,\frac{{(az)_\infty (b)_\infty }} {{(c)_\infty (z)_\infty }}\,2^\Phi 1\,\left( {{}_{az}^{{c \mathord{\left/ {\vphantom {c {b,\,z}}} \right. \kern-\nulldelimiterspace} {b,\,z}}} ;\,b} \right),} & {|b|,\,|z|} \\ \end{array} \, < \,1,$$
(1)
and second to characterize the symmetric polynomials introduced by L. J. Rogers [8] in 1893.

Keywords

Discrete Analogue Symmetric Polynomial Basic Hypergeometric Series Important Transformation CBMS Regional Conference Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • Douglas Bowman
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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