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.