Recurrence Relations, Continued Fractions and Orthogonal Polynomials
Richard Askey · Mourad Ismail
jan. 1984 · American Mathematical Society: Memoirs of the American Mathematical Society 300. knjiga · American Mathematical Soc.
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We address the question of recovering the distribution function of a set of orthogonal polynomials from the three term recurrence relation satisfied by the polynomials. We investigate four sets of orthogonal polynomials: the Al-Salam-Chihara polynomials, random walk polynomials and their [italic]q-analogue, and the case [italic]q = -1 of the associated continuous [italic]q-ultraspherical polynomials. For each polynomial set we obtain generating functions, derive explicit representations as ordinary or basic hypergeometric functions and determine their asymptotic behavior
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