ISSN:
1432-0940
Keywords:
Primary 39A10
;
40A15
;
30B70
;
30B40
;
Secondary 40A05
;
11B37
;
Explicit solutions to linear difference equations and their asymptotic behavior
;
Convergence of continued fractions
;
Analytic continuation
;
Convergence of recurrent sequences
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract For any system of linear difference equations of arbitrary order, a family of solution formulas is constructed explicitly by way of relating the given system to simpler neighboring systems. These formulas are then used to investigate the asymptotic behavior of the solutions. When applying this difference equation method to second-order equations that belong to neighboring continued fractions, new results concerning convergence of continued fractions as well as meromorphic extension of analytic continued fractions beyond their convergence region are provided. This is demonstrated for analytic continued fractions whose elements tend to infinity. Finally, a recent result on the existence of limits of solutions to real difference equations having infinite order is extended to complex equations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01263065
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