Difference between revisions of "Bernoulli numbers"

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(Created page with "The Bernoulli numbers are the numbers $B_n$ in the following formula: $$\dfrac{z}{e^z-1} = \displaystyle\sum_{k=0}^{\infty} B_k \dfrac{z^k}{k!}.$$ The Bernoulli numbers are in...")
 
 
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The Bernoulli numbers are the numbers $B_n$ in the following formula:
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The Bernoulli numbers are the numbers $B_n$ in the following formula $z<2\pi$:
 
$$\dfrac{z}{e^z-1} = \displaystyle\sum_{k=0}^{\infty} B_k \dfrac{z^k}{k!}.$$
 
$$\dfrac{z}{e^z-1} = \displaystyle\sum_{k=0}^{\infty} B_k \dfrac{z^k}{k!}.$$
The Bernoulli numbers are intimately related to the [[Bernoulli polynomial|Bernoulli polynomials]].
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=See Also=
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[[Bernoulli polynomial|Bernoulli polynomials]]
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=References=
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* {{BookReference|Higher Transcendental Functions Volume I|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=Gamma function written as infinite product|next=Euler-Mascheroni constant}}: §1.13 (1)
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[[Category:SpecialFunction]]

Latest revision as of 23:23, 3 March 2018

The Bernoulli numbers are the numbers $B_n$ in the following formula $z<2\pi$: $$\dfrac{z}{e^z-1} = \displaystyle\sum_{k=0}^{\infty} B_k \dfrac{z^k}{k!}.$$

See Also

Bernoulli polynomials

References