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Date: 23-9-2019
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Date: 15-5-2018
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Date: 23-8-2018
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Polynomials which form a Sheffer sequence with
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(1) |
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(2) |
giving generating function
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(3) |
Roman (1984) defines Bernoulli numbers of the second kind as . They are related to the Stirling numbers of the first kind
by
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(4) |
(Roman 1984, p. 115), and obey the reflection formula
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(5) |
(Roman 1984, p. 119).
The first few Bernoulli polynomials of the second kind are
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(6) |
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(7) |
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(8) |
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(9) |
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(10) |
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.
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