Meromorphic functions with prescribed asymptotic behaviour, zeros and poles and applications in complex approximation

1999 ◽  
Vol 51 (1) ◽  
pp. 117-129
Author(s):  
A. Sauer
Keyword(s):  
Power Series ◽  
Asymptotic Behaviour ◽  
Series Expansion ◽  
Meromorphic Functions ◽  
Power Series Expansion ◽  
Complex Approximation ◽  
Asymptotic Power ◽  
Approximation Theorems ◽  
Zeros And Poles

AbstractWe construct meromorphic functions with asymptotic power series expansion in z−1 at ∞ on an Arakelyan set A having prescribed zeros and poles outside A. We use our results to prove approximation theorems where the approximating function fulfills interpolation restrictions outside the set of approximation.

Asymptotics of the Titchmarsh-Weyl m-coefficient for integrable potentials

1986 ◽  
Vol 103 (3-4) ◽  
pp. 347-358 ◽  
Author(s):  
Hans G. Kaper ◽  
Man Kam Kwong
Keyword(s):  
Asymptotic Expansion ◽  
Power Series ◽  
Asymptotic Behaviour ◽  
Potential Function ◽  
Error Bound ◽  
Power Series Expansion ◽  
Smoothness Condition ◽  
Asymptotic Power ◽  
Simple Method ◽  
Expansion Coefficients

This article is concerned with the asymptotic behaviour of m(λ), the Titchmarsh-Weyl m-coefficient, for the singular eigenvalue equation y“ + (λ − q(x))y = 0 on [0, ∞), as λ →∞ in a sector in the upper half of the complex plane. It is assumed that the potential function q is integrable near 0. A simplified proof is given of a result of Atkinson [7], who derived the first two terms in the asymptotic expansion of m(λ), and a sharper error bound is obtained. Theproof is then generalised to derive subsequent terms in the asymptotic expansion. It is shown that the Titchmarsh-Weyl m-coefficient admits an asymptotic power series expansion if the potential function satisfies some smoothness condition. A simple method to compute the expansion coefficients is presented. The results for the first few coefficients agree with those given by Harris [9].

scholarly journals Identities Involving the Fourth-Order Linear Recurrence Sequence

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1476 ◽  
Author(s):  
Lan Qi ◽  
Zhuoyu Chen
Keyword(s):  
Power Series ◽  
Series Expansion ◽  
Generating Function ◽  
Fourth Order ◽  
Power Series Expansion ◽  
Linear Recurrence ◽  
Recurrence Sequence ◽  
Order Linear ◽  
Elementary Methods ◽  
Linear Recurrence Sequence

In this paper, we introduce the fourth-order linear recurrence sequence and its generating function and obtain the exact coefficient expression of the power series expansion using elementary methods and symmetric properties of the summation processes. At the same time, we establish some relations involving Tetranacci numbers and give some interesting identities.

Analytic Structure and Power-Series Expansion of the Jost Matrix

2012 ◽  
Vol 54 (5-6) ◽  
pp. 673-683
Author(s):  
S. A. Rakityansky ◽  
N. Elander
Keyword(s):  
Power Series ◽  
Series Expansion ◽  
Power Series Expansion ◽  
Analytic Structure
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