Polynomials which form a Sheffer
sequence with
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
See also
Bernoulli Number of the Second Kind,
Bernoulli Polynomial,
Sheffer Sequence,
Stirling
Number of the First Kind
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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.Referenced
on Wolfram|Alpha
Bernoulli Polynomial
of the Second Kind
Cite this as:
Weisstein, Eric W. "Bernoulli Polynomial of the Second Kind." From MathWorld--A Wolfram Web Resource.
https://mathworld.wolfram.com/BernoulliPolynomialoftheSecondKind.html
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