Abstract
By using the monomiality principle and general results on Sheffer polynomial sets, the differential equation satisfied by several old and new polynomial sets is shown.
Highlights
A uniform method is presented for constructing the differential equations satisfied by several sets of classical and non classical polynomials
This has been done by starting from the basic elements of the relevant generating functions, using the monomiality principle by
In our case, we are dealing with a Sheffer polynomial set, so that, since we have ψ(t) = et, the operator σ defined by Equation (6) reduces to the derivative operator Dx
Summary
A uniform method is presented for constructing the differential equations satisfied by several sets of classical and non classical polynomials. This has been done by starting from the basic elements of the relevant generating functions, using the monomiality principle by. The polynomials considered in this paper are only examples for showing that the method works, but obviously this technique can be theoretically extended to every polynomial set This method has been recently applied in several articles (see [3,4,5,6,7,8,9]), which include works in collaboration with several authors.
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