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).
Read more about this topic: Binomial Type
Famous quotes containing the word identity:
“Adultery is the vice of equivocation.
It is not marriage but a mockery of it, a merging that mixes love and dread together like jackstraws. There is no understanding of contentment in adultery.... You belong to each other in what together you’ve made of a third identity that almost immediately cancels your own. There is a law in art that proves it. Two colors are proven complimentary only when forming that most desolate of all colors—neutral gray.”
—Alexander Theroux (b. 1940)