Pidduck Polynomial

Polynomials  which form the Sheffer sequence for

			(1)
			(2)

and have generating function

(3)

The first few are

			(4)
			(5)
			(6)
			(7)

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

(8)

(Roman 1984, p. 127).

REFERENCES:

Bateman, H. "The Polynomial of Mittag-Leffler." Proc. Nat. Acad. Sci. USA 26, 491-496, 1940.

Boas, R. P. and Buck, R. C. Polynomial Expansions of Analytic Functions, 2nd print., corr. New York: Academic Press, p. 38, 1964.

Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. Higher Transcendental Functions, Vol. 3. New York: Krieger, p. 248, 1981.

Roman, S. The Umbral Calculus. New York: Academic Press, 1984.