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Stirling Polynomial

المؤلف:  Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G

المصدر:  Higher Transcendental Functions, Vol. 3. New York: Krieger

الجزء والصفحة:  ...

23-9-2019

1783

Stirling Polynomial

 

Polynomials  which form the Sheffer sequence for

			(1)
			(2)

where  is the inverse function of , and have generating function

(3)

The first few polynomials are

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

The Stirling polynomials are related to the Stirling numbers of the first kind  by

(8)

where  is a binomial coefficient and  is an integer with  (Roman 1984, p. 129).

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REFERENCES:

Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. Higher Transcendental Functions, Vol. 3. New York: Krieger, p. 257, 1981.

Roman, S. "The Stirling Polynomials." §4.8 in The Umbral Calculus. New York: Academic Press, pp. 128-129, 1984.