Binomial Type - Characterization By A Convolution Identity

Characterization By A Convolution Identity

For sequences an, bn, n = 0, 1, 2, ..., define a sort of convolution by

Let be the nth term of the sequence

Then for any sequence ai, i = 0, 1, 2, ..., with a0 = 0, the sequence defined by p0(x) = 1 and

for n ≥ 1, is of binomial type, and every sequence of binomial type is of this form. This result is due to Alessandro di Bucchianico (see References below).

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