The leading term of the PlancherelRotach asymptotic formula for solutions of recurrence relations
Abstract
Recurrence relations generating Padé and HermitePadé 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 PlancherelRotach 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 fourterm relations. For threeterm recurrence relations this result generalizes a theorem Van Assche obtained for recurrence relations with 'regularly' growing coefficients. Bibliography: 19 titles.
 Authors:
 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
Citation Formats
Aptekarev, A I, and Tulyakov, D N. The leading term of the PlancherelRotach asymptotic formula for solutions of recurrence relations. United States: N. p., 2014.
Web. doi:10.1070/SM2014V205N12ABEH004435.
Aptekarev, A I, & Tulyakov, D N. The leading term of the PlancherelRotach asymptotic formula for solutions of recurrence relations. United States. doi:10.1070/SM2014V205N12ABEH004435.
Aptekarev, A I, and Tulyakov, D N. 2014.
"The leading term of the PlancherelRotach asymptotic formula for solutions of recurrence relations". United States.
doi:10.1070/SM2014V205N12ABEH004435.
@article{osti_22364154,
title = {The leading term of the PlancherelRotach asymptotic formula for solutions of recurrence relations},
author = {Aptekarev, A I and Tulyakov, D N},
abstractNote = {Recurrence relations generating Padé and HermitePadé 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 PlancherelRotach 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 fourterm relations. For threeterm recurrence relations this result generalizes a theorem Van Assche obtained for recurrence relations with 'regularly' growing coefficients. Bibliography: 19 titles.},
doi = {10.1070/SM2014V205N12ABEH004435},
journal = {Sbornik. Mathematics},
number = 12,
volume = 205,
place = {United States},
year = 2014,
month =
}

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