Mikusinski’s operators solution of three-order linear difference equation with variable coefficients

1994 ◽  
Vol 15 (1) ◽  
pp. 71-79
Author(s):  
Zhou Zhi-hu
Keyword(s):  
Difference Equation ◽  
Linear Difference Equation ◽  
Variable Coefficients ◽  
Order Linear

Difference equations, determinants and the Secret Santa problem

2005 ◽  
Vol 89 (514) ◽  
pp. 2-6
Author(s):  
Tony Ward
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Linear Difference Equation ◽  
Variable Coefficients ◽  
Second Order ◽  
Auxiliary Equation ◽  
Order Linear ◽  
Particular Solution

In [1] it is shown that every second-order linear difference equation with, in general, variable coefficients can be reduced to the formIt is also shown that (1) can be solved explicitly provided that a particular solution a (n) of the ‘auxiliary equation’can be found, and many cases in which a solution of (2) is available are discussed. However, [1] is defective in that no method of finding a solution of (2) in the general case is given.

Fibonacci and Lucas polynomials

1981 ◽  
Vol 90 (3) ◽  
pp. 385-387 ◽  
Author(s):  
B. G. S. Doman ◽  
J. K. Williams
Keyword(s):  
Difference Equation ◽  
Chebyshev Polynomials ◽  
Generating Functions ◽  
Hypergeometric Functions ◽  
Linear Difference Equation ◽  
Second Order ◽  
Lucas Numbers ◽  
Order Linear ◽  
Lucas Polynomials ◽  
Fibonacci And Lucas Numbers

The Fibonacci and Lucas polynomials Fn(z) and Ln(z) are denned. These reduce to the familiar Fibonacci and Lucas numbers when z = 1. The polynomials are shown to satisfy a second order linear difference equation. Generating functions are derived, and also various simple identities, and relations with hypergeometric functions, Gegenbauer and Chebyshev polynomials.

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