A NOTE ON THE LOCAL STABILITY OF THE GENERAL FIRST ORDER DIFFERENCE EQUATION

1976 ◽  
Vol 44 (2) ◽  
pp. 182-184 ◽  
Author(s):  
R. W. FAREBROTHER
Keyword(s):  
Difference Equation ◽  
Local Stability ◽  
Order Difference ◽  
First Order ◽  
Order Difference Equation

AN OSCILLATION CRITERION FOR FIRST ORDER DIFFERENCE EQUATION

2020 ◽  
Vol 33 (01) ◽  
Author(s):  
Thaniyarasu Kumar ◽  
◽  
Govindasamy Ayyappan ◽  
Keyword(s):  
Difference Equation ◽  
Oscillation Criterion ◽  
Order Difference ◽  
First Order ◽  
Order Difference Equation

scholarly journals DIFFERENCE EQUATION OF THE COLORED JONES POLYNOMIAL FOR TORUS KNOT

2004 ◽  
Vol 15 (09) ◽  
pp. 959-965 ◽  
Author(s):  
KAZUHIRO HIKAMI
Keyword(s):  
Difference Equation ◽  
Jones Polynomial ◽  
Order Difference ◽  
Colored Jones Polynomial ◽  
First Order ◽  
Torus Knot ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
Hypergeometric Type ◽  
The Difference

We prove that the N-colored Jones polynomial for the torus knot [Formula: see text] satisfies the second order difference equation, which reduces to the first order difference equation for a case of [Formula: see text]. We show that the A-polynomial of the torus knot can be derived from the difference equation. Also constructed is a q-hypergeometric type expression of the colored Jones polynomial for [Formula: see text].

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