Matrix-valued little q-Jacobi polynomials

• Noud Aldenhoven ^[1] ; Erik Koelink ^[1] ; Ana M. de los Ríos ^[2]
  1. [1] Radboud University Nijmegen

     Radboud University Nijmegen

     Países Bajos

     
  2. [2] Universidad de Sevilla

     Universidad de Sevilla

     Sevilla, España

     
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 193, Nº 1 (May 2015), 2015, págs. 164-183
• Idioma: inglés
• DOI: 10.1016/j.jat.2014.10.007
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• Resumen

  • Matrix-valued analogues of the little q-Jacobi polynomials are introduced and studied. For the 2×2-matrix-valued little q-Jacobi polynomials explicit expressions for the orthogonality relations, Rodrigues formula, three-term recurrence relation and their relation to matrix-valued q-hypergeometric series and the scalar-valued little q-Jacobi polynomials are presented. The study is based on a matrix-valued q-difference operator, which is a q-analogue of Tirao’s matrix-valued hypergeometric differential operator.