Polynomials | Factorial and binomial topics

Binomial type

In mathematics, a polynomial sequence, i.e., a sequence of polynomials indexed by non-negative integers in which the index of each polynomial equals its degree, is said to be of binomial type if it satisfies the sequence of identities Many such sequences exist. The set of all such sequences forms a Lie group under the operation of umbral composition, explained below. Every sequence of binomial type may be expressed in terms of the Bell polynomials. Every sequence of binomial type is a Sheffer sequence (but most Sheffer sequences are not of binomial type). Polynomial sequences put on firm footing the vague 19th century notions of umbral calculus. (Wikipedia).

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Related pages

Lie group | List of factorial and binomial topics | Moment (mathematics) | Delta operator | Statistics | Sheffer sequence | Probability | Empty product | Group (mathematics) | Polynomial | Umbral calculus | Combinatorics | Exponential function | Poisson distribution | Degree of a polynomial | Cauchy product | Polynomial sequence | Binomial theorem | Touchard polynomials | Faà di Bruno's formula | Mathematics | Bell polynomials | Power series | Probability distribution | Constant term | Stirling number | Convolution | Random variable | Abel polynomials | Generating function | Cumulant