Hyperdifferential representation of polynomial sequences
Abstract
We introduce a representation of polynomial sequences {pn(z)}∞n=0 in the form pn(z) = eG(z)zn , where G(z) is some differential operator, a representation we refer to as hyperdifferential representation. Such representation exists for sequences with p0(z) = 1. It is outlined how the generator of representation G(z) is obtained. The method is applied to the Laguerre polynomials and new identities involving sums of them are obtained.
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