Difference between revisions of "Digamma at n+1"

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(Created page with "==Theorem== The following formula holds: $$\psi(n+1)=1+\dfrac{1}{2}+\dfrac{1}{3}+\ldots+\dfrac{1}{n} - \gamma=H_n - \gamma,$$ where $\psi$ denotes the digamma function and...")
 
 
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==References==
 
==References==
* {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=Digamma functional equation|next=findme}}: $\S 1.7 (9)$
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* {{BookReference|Higher Transcendental Functions Volume I|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=Digamma functional equation|next=Digamma at z+n}}: $\S 1.7 (9)$
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Digamma at 1|next=Digamma at 1/2}}: $6.3.2$
  
 
[[Category:Theorem]]
 
[[Category:Theorem]]
 
[[Category:Unproven]]
 
[[Category:Unproven]]

Latest revision as of 23:22, 3 March 2018

Theorem

The following formula holds: $$\psi(n+1)=1+\dfrac{1}{2}+\dfrac{1}{3}+\ldots+\dfrac{1}{n} - \gamma=H_n - \gamma,$$ where $\psi$ denotes the digamma function and $\gamma$ denotes the Euler-Mascheroni constant, and $H_n$ is the $n$th harmonic number.

Proof

References