Difference between revisions of "Harmonic number"

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(Created page with "The Harmonic numbers $\mathbb{H}=\{H_0,H_1,H_2,\ldots\}$ are defined by the formula $$H_n = \displaystyle\sum_{k=0}^n \dfrac{1}{k}.$$")
 
 
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The Harmonic numbers $\mathbb{H}=\{H_0,H_1,H_2,\ldots\}$ are defined by the formula
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The Harmonic numbers $\{H_1,H_2,\ldots\}$ are defined by the formula
$$H_n = \displaystyle\sum_{k=0}^n \dfrac{1}{k}.$$
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$$H_n = \displaystyle\sum_{k=1}^n \dfrac{1}{k}=1+\dfrac{1}{2}+\dfrac{1}{3}+\ldots+\dfrac{1}{n}.$$
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=Properties=
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=References=
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* {{BookReference|Special Functions|1960|Earl David Rainville|prev=Euler-Mascheroni constant|next=findme}}: $7.(2)$
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[[Category:SpecialFunction]]

Latest revision as of 03:12, 5 January 2017

The Harmonic numbers $\{H_1,H_2,\ldots\}$ are defined by the formula $$H_n = \displaystyle\sum_{k=1}^n \dfrac{1}{k}=1+\dfrac{1}{2}+\dfrac{1}{3}+\ldots+\dfrac{1}{n}.$$

Properties

References