Asymptotic behavior of solutions of general three term recurrence relations
نویسندگان
چکیده
منابع مشابه
Asymptotic behavior of solutions of general three term recurrence relations
We consider the solutions of general three term recurrence relations whose coefficients are analytic functions in a prescribed region. We study the ratio asymptotic of such solutions under the assumption that the coefficients are asymptotically periodic and their strong asymptotic under more restrictive conditions.
متن کاملComputational properties of three-term recurrence relations for Kummer functions
Several three-term recurrence relations for confluent hypergeometric functions are analyzed from a numerical point of view. Minimal and dominant solutions for complex values of the variable z are given, derived from asymptotic estimates of Whittaker functions with large parameters. The Laguerre polynomials and the regular Coulomb wave functions are studied as particular cases, with numerical ex...
متن کاملSolutions of Three - Term Relations in Several Variables
A system of multivariate orthogonal polynomials satisfies a matrix equation which plays the role of a three-term relation of the orthogonal polynomial of one variable. However, unlike the case of one variable, there does not exist a second solution of this matrix equation that is linearly independent to the orthogonal polynomials. In particular, there is no analogy of the associated polynomials...
متن کاملEigenstructure of Order-One-Quasiseparable Matrices. Three-term and Two-term Recurrence Relations
This paper presents explicit formulas and algorithms to compute the eigenvalues and eigenvectors of order-one-quasiseparable matrices. Various recursive relations for characteristic polynomials of their principal submatrices are derived. The cost of evaluating the characteristic polynomial of an N × N matrix and its derivative is only O(N). This leads immediately to several versions of a fast q...
متن کاملRecurrence and Asymptotic Relations of a Generalized Elliptic-type Integral
Epstein-Hubbell 1963 elliptic-type integrals occur in radiation field problems. In this paper, we consider a generalization of the elliptic-type integrals introduced by Kalla and Tuan 1996 and developed by Salman 2006. We give some recurrence relations for this generalized special function. Some of these relations can be used for analytic continuation to different domains. Asymptotic relations ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Computational Mathematics
سال: 2006
ISSN: 1019-7168,1572-9044
DOI: 10.1007/s10444-004-4137-x