Abstract
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 x 2 non-autonomous matrices. The solutions of the decoupled
equations are factorial polynomials.
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