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Bernoulli Polynomial of the Second Kind

المؤلف:  Roman, S.

المصدر:  "The Bernoulli Polynomials of the Second Kind." §5.3.2 in The Umbral Calculus. New York: Academic Press

الجزء والصفحة:  pp. 113-119

15-9-2019

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Bernoulli Polynomial of the Second Kind

Polynomials  which form a Sheffer sequence with

			(1)
			(2)

giving generating function

(3)

Roman (1984) defines Bernoulli numbers of the second kind as . They are related to the Stirling numbers of the first kind  by

(4)

(Roman 1984, p. 115), and obey the reflection formula

(5)

(Roman 1984, p. 119).

The first few Bernoulli polynomials of the second kind are

			(6)
			(7)
			(8)
			(9)
			(10)

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REFERENCES:

Roman, S. "The Bernoulli Polynomials of the Second Kind." §5.3.2 in The Umbral Calculus. New York: Academic Press, pp. 113-119, 1984.