$q$-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions

Released on by Douglas Bowman
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  • $q$-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions Book Detail

  • Author : Douglas Bowman
  • Release Date : 2002
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 73
  • ISBN 13 : 082182774X
  • File Size : 27,27 MB
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$q$-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions by Douglas Bowman PDF Summary

Book Description: The author explores ramifications and extensions of a $q$-difference operator method first used by L.J. Rogers for deriving relationships between special functions involving certain fundamental $q$-symmetric polynomials. In special cases these symmetric polynomials reduce to well-known classes of orthogonal polynomials. A number of basic properties of these polynomials follow from this approach. This leads naturally to the evaluation of the Askey-Wilson integral and generalizations. Expansions of certain generalized basic hypergeometric functions in terms of the symmetric polynomials are also found. This provides a quick route to understanding the group structure generated by iterating the two-term transformations of these functions. Some infrastructure is also laid for more general investigations in the future

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