An asymptotic analysis of nonoscillatory solutions of q-difference equations via q-regular variation
TLDR
In this article, a thorough asymptotic analysis of nonoscillatory solutions of the q-difference equation D q ( r ( t ) D q y (t ) + p( t ) y ( q t ) = 0 considered on the lattice { q k : k ∈ N 0 }, q > 1 ǫ, q > 0,About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2017-10-15 and is currently open access. It has received 10 citations till now. The article focuses on the topics: Asymptotic analysis & Method of matched asymptotic expansions.read more
Citations
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The Karamata integration theorem on time scales and its applications in dynamic and difference equations
TL;DR: A time scale version of the well-known result from the theory of regular variation, namely the Karamata integration theorem, is derive and a classification and asymptotic formulae for all (positive) solutions are obtained, which unify, extend, and improve the existing results.
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Refined discrete regular variation and its applications
TL;DR: In this article, a new class of regular varying sequences with respect to an auxiliary sequence is introduced, and the properties of these sequences are investigated. But the authors focus on regular variation on time scales.
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Properties of critical and subcritical second order self-adjoint linear equations
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Existence of positive strongly decaying solutions of second-order nonlinear q-difference equations
TL;DR: In this article, the existence of positive strongly decaying solutions of second-order nonlinear q-difference equation was investigated and it was shown that the strongly decaying solution of the second order non-linear qdifference problem can be found in the form
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Kummer test and regular variation
TL;DR: In this paper, a new interpretation of the Kummer test is given, which detects convergence of series, based on the refined regularly varying sequences with respect to an auxiliary sequence, and the theory of such sequences can be developed by transforming them into the new time scale, which then enables us to utilize the existing results for regularly varying functions on time scales.
References
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Book
Basic Hypergeometric Series
George Gasper,Mizan Rahman +1 more
TL;DR: In this article, the Askey-Wilson q-beta integral and some associated formulas were used to generate bilinear generating functions for basic orthogonal polynomials.
Book
Dynamic Equations on Time Scales: An Introduction with Applications
Martin Bohner,Allan Peterson +1 more
TL;DR: The Time Scales Calculus as discussed by the authors is a generalization of the time-scales calculus with linear systems and higher-order linear equations, and it can be expressed in terms of linear Symplectic Dynamic Systems.
BookDOI
Special functions of mathematical physics : a unified introduction with applications
TL;DR: The theory of classical or thogonal polynomials of a discrete variable on both uniform and non-uniform lattices has been given a coherent presentation, together with its various applications in physics as discussed by the authors.
Book
Hypergeometric Orthogonal Polynomials and Their q-Analogues
TL;DR: In this paper, Orthogonal Polynomial Solutions of Differential Equations of Real Difference Equations (DDEs) were used to solve Eigenvalue Problems. But they were not used in the context of orthogonal polynomials.