A polynomial
given by the associated Sheffer sequence with

(1)

given by

(2)

The generating function is

(3)

where
is the Lambert W-function . The associated binomial identity is

(4)

where
is a binomial coefficient , a formula originally
due to Abel (Riordan 1979, p. 18; Roman 1984, pp. 30 and 73).

The first few Abel polynomials are

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References Riordan, J. Combinatorial Identities. New York: Wiley, p. 18, 1979. Roman, S. "The
Abel Polynomials." §4.1.5 in The
Umbral Calculus. New York: Academic Press, pp. 29-30 and 72-75, 1984. Referenced
on Wolfram|Alpha Abel Polynomial
Cite this as:
Weisstein, Eric W. "Abel Polynomial."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/AbelPolynomial.html

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