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Title: The leading term of the Plancherel-Rotach asymptotic formula for solutions of recurrence relations

Recurrence relations generating Padé and Hermite-Padé polynomials are considered. Their coefficients increase with the index of the relation, but after dividing by an appropriate power of the scaling function they tend to a finite limit. As a result, after scaling the polynomials 'stabilize' for large indices; this type of asymptotic behaviour is called Plancherel-Rotach asymptotics. An explicit expression for the leading term of the asymptotic formula, which is valid outside sets containing the zeros of the polynomials, is obtained for wide classes of three- and four-term relations. For three-term recurrence relations this result generalizes a theorem Van Assche obtained for recurrence relations with 'regularly' growing coefficients. Bibliography: 19 titles.
Authors:
;  [1]
  1. M.V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
22364154
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 12; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ASYMPTOTIC SOLUTIONS; INDEXES; PADE APPROXIMATION; POLYNOMIALS; RECURSION RELATIONS