Difference between revisions of "Digamma at n+1"
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==References== | ==References== | ||
| − | * {{BookReference|Higher Transcendental Functions Volume I|1953| | + | * {{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}}: $\S 1.7 (9)$ |
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Digamma at 1|next=Digamma at 1/2}}: $6.3.2$ | * {{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
- 1953: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.7 (9)$
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $6.3.2$
