A unified construction of all the hypergeometric and basic hypergeometric families of orthogonal polynomial sequences

19 Feb 2020 Luis Verde-Star

We construct a set $H$ of orthogonal polynomial sequences that contains all the families in the Askey scheme and the $q$-Askey scheme. The polynomial sequences in $H$ are solutions of a generalized first-order difference equation which is determined by three linearly recurrent sequences of numbers... (read more)

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Categories


  • CLASSICAL ANALYSIS AND ODES
  • 33C45, 33D45