Plancherel-Rotach type asymptotics for solutions of linear recurrence relations with rational coefficients

Journal Article · Thu Nov 11 00:00:00 EST 2010 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2010V201N09ABEH004115· OSTI ID:21418069

Tulyakov, Dmitrii N ^[1]

---

1. M.V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow (Russian Federation)

The asymptotic behaviour of solutions of difference equations with respect to the variable n with spectral parameter x is investigated. A new method for finding asymptotic expansions for basis solutions in overlapping domains of the (n,x)-space which extend to infinity is proposed. In principle, matching the expansions in the intersection of these domains makes it possible to determine the global asymptotic picture of the behaviour of solutions of equations in the complex plane of the spectral parameter x for suitable scaling depending on n. The potential of the method is demonstrated using the examples of the Hermite and Meixner polynomials. Bibliography: 27 titles.

• OSTI ID: 21418069
• Journal Information: Sbornik. Mathematics, Vol. 201, Issue 9; Other Information: DOI: 10.1070/SM2010v201n09ABEH004115; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ASYMPTOTIC SOLUTIONS
BIBLIOGRAPHIES
EQUATIONS
MATHEMATICAL SPACE
POLYNOMIALS
RECURSION RELATIONS
DOCUMENT TYPES
FUNCTIONS
MATHEMATICAL SOLUTIONS
SPACE