basic polynomial sequence - Wolfram|Alpha

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Input interpretation

basic polynomial sequence

Definition

A polynomial sequence p_n(x) is called the basic polynomial sequence for a delta operator Q if
1.p_0(x) = 1, 2.p_n(0) = 0 for all n>0, 3.Q p_n(x) = n p_(n - 1)(x).
If p_n(x) is a basic polynomial sequence for some delta operator Q, then it is a binomial-type sequence of polynomials. Furthermore, if p_n(x) is a binomial-type sequence of polynomials, then it is a basic polynomial sequence for some delta operator.

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Related terms

binomial-type sequence | delta operator | polynomial sequence | umbral operator

Subject classifications

MathWorld

umbral calculus

MSC 2010

05A40

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