Recursive formulation of the relativistic law of superposition of multiple collinear velocities

We study the recursive formulation of the law of superposition of multiple collinear velocities. We start with the non-linear equation, transform it into two linear coupled difference equations with variable cofficients, and then decouple these latter equations. The coupled difference equations are...

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Vydáno v:Journal of difference equations and applications Ročník 13; číslo 7; s. 563 - 575
Hlavní autor: Antippa, Adel F.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Taylor & Francis Group 01.07.2007
Témata:
03D80 (Applications of computability and recursion theory)
05A10 (Factorials, binomial coefficients, combinatorial functions)
05C20 (Directed graphs)
05C38 (Paths and cycles)
05C90 (Applications of Graph Theory)
39A10 (Difference Equations)
83A05 (Special relativity)
Difference equations
Directed graphs
Factorial polynomials
Matrix Pochhammers
Paths and cycles
Recursion relations
ISSN:1023-6198, 1563-5120
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Shrnutí:We study the recursive formulation of the law of superposition of multiple collinear velocities. We start with the non-linear equation, transform it into two linear coupled difference equations with variable cofficients, and then decouple these latter equations. The coupled difference equations are solved by three different, but interrelated, methods: (i) via the graph theoretic discrete path approach, (ii) by using the general closed form solution of two coupled first order difference equations with variable coefficients, and (iii) in terms of the symmetric functions via the pochhammers of 2 × 2 non-autonomous matrices. The solutions of the decoupled equations are factorial polynomials.
Bibliografie:ObjectType-Article-2
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ObjectType-Feature-1
content type line 23
ISSN:1023-6198
1563-5120
DOI:10.1080/10236190701264701