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Second order linear difference equations

Author
Encinas, A.; Jiménez, M.J.
Type of activity
Journal article
Journal
Journal of difference equations and applications
Date of publication
2017-12-04
Volume
24
Number
3
First page
305
Last page
343
DOI
https://doi.org/10.1080/10236198.2017.1408608 Open in new window
Repository
http://hdl.handle.net/2117/112719 Open in new window
URL
http://www.tandfonline.com/doi/abs/10.1080/10236198.2017.1408608?journalCode=gdea20 Open in new window
Abstract
We provide the explicit solution of a general second order linear difference equation via the computation of its associated Green function. This Green function is completely characterized and we obtain a closed expression for it using functions of two–variables, that we have called Chebyshev functions due to its intimate relation with the usual one–variable Chebyshev polynomials. In fact, we show that Chebyshev functions become Chebyshev polynomials if constant coefficients are considered.
Citation
Encinas, A., Jiménez, M.J. Second order linear difference equations. "Journal of difference equations and applications", 4 Desembre 2017, p. 1-39.
Keywords
Chebyshev functions, Chebyshev polynomials, Second order difference equations, green function, initial value problem
Group of research
MAPTHE - Matrix Analysis and Discrete Potential Theory

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