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Published online by Cambridge University Press: 20 January 2009
Let f(x) and F(x) be polynomials which are supposed to be decomposed into a series of n terms as
Further let θ be a distributive operation and φ(x) be a given function. Then the functional equation
has a solution of the form
where yν (x) (ν = 1, 2, … n) is the solution of the equation
Proc. Edinburgh Math. Soc., XLII (1924), 95–103.
* The demonstration of the equation (2), with certain results belonging to the calculus of differences are given by the author in the paper, “O redukol , Casopis, 54, Praha (in the press).