Polynomials
which form the associated Sheffer sequence for

(1)

and have the generating function

(2)

An explicit formula is given by

(3)

where
is a falling factorial , which can be summed
in closed form in terms of the hypergeometric
function , gamma function , and polygamma
function . The binomial identity associated with the Sheffer
sequence is

(4)

The Mittag-Leffler polynomials satisfy the recurrence formula

(5)

The first few Mittag-Leffler polynomials are

The Mittag-Leffler polynomials are related to the Pidduck
polynomials by

(11)

(Roman 1984, p. 127).

See also Pidduck Polynomial
Explore with Wolfram|Alpha
References Bateman, H. "The Polynomial of Mittag-Leffler." Proc. Nat. Acad. Sci. USA 26 , 491-496, 1940. Roman, S.
"The Mittag-Leffler Polynomials." §4.1.6 in The
Umbral Calculus. New York: Academic Press, pp. 75-78 and 127, 1984. Referenced
on Wolfram|Alpha Mittag-Leffler Polynomial
Cite this as:
Weisstein, Eric W. "Mittag-Leffler Polynomial."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/Mittag-LefflerPolynomial.html

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