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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In this work, we construct the transformation operator for the infinite system of the difference equations $a_{n-2}y_{n-2}+b_{n-1}y_{n-1}+c_{n}y_{n}+b_{n}y_{n+1}+a_{n}y_{n+2}=lambda y_{n}$ $(n=1,2,...)$,where $a_{n}neq0,$ $b_{n},$ $c_{n}$ $(n=1,2,3,...)$ are given complex numbers, investigate some important properties of the special solutions of the difference system.
📌 3 Key Takeaways
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Objective & Hypothesis:In this work, we construct the transformation operator for the infinite system of the difference equations $a_{n-2}y_{n-2}+b_{n-1}y_{n-1}+c_{n}y_{n}+b_{n}y_{n+1}+a_{n}y_{n+2}=lambda y_{n}$ $(n=1,2,...)$,where $a_{n}neq0,$ $b_{n},$ $c_{n}$ $(n=1,2,3,...)$ are given complex numbers, investigate some important properties of the special solutions of the difference system.
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Key Findings & Data:In this work, we construct the transformation operator for the infinite system of the difference equations $a_{n-2}y_{n-2}+b_{n-1}y_{n-1}+c_{n}y_{n}+b_{n}y_{n+1}+a_{n}y_{n+2}=lambda y_{n}$ $(n=1,2,...)$,where $a_{n}neq0,$ $b_{n},$ $c_{n}$ $(n=1,2,3,...)$ are given complex numbers, investigate some important properties of the special solutions of the difference system.
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Conclusion & Impact:In this work, we construct the transformation operator for the infinite system of the difference equations $a_{n-2}y_{n-2}+b_{n-1}y_{n-1}+c_{n}y_{n}+b_{n}y_{n+1}+a_{n}y_{n+2}=lambda y_{n}$ $(n=1,2,...)$,where $a_{n}neq0,$ $b_{n},$ $c_{n}$ $(n=1,2,3,...)$ are given complex numbers, investigate some important properties of the special solutions of the difference system.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this work, we construct the transformation operator for the infinite system of the difference equations $a_{n-2}y_{n-2}+b_{n-1}y_{n-1}+c_{n}y_{n}+b_{n}y_{n+1}+a_{n}y_{n+2}=lambda y_{n}$ $(n=1,2,...)$,where $a_{n}neq0,$ $b_{n},$ $c_{n}$ $(n=1,2,3,...)$ are given complex numbers, investigate some important properties of the special solutions of the difference system.
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Cite This Article
GÜRDAL, M., NABİYEV, A. A. (2022). On The Solution of an Infinite System of Discrete Equations. Turkish Journal of Mathematics and Computer Science, Cilt: 12 - Sayı: 2, 157–160. https://ajindex.com/articles/609116