Difference between revisions of "Digamma at n+1/2"
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(Created page with "==Theorem== The following formula holds for $n=1,2,3,\ldots$: $$\psi \left( n +\dfrac{1}{2} \right) = -\gamma - 2 \log(2)+ 2 \left( 1 + \dfrac{1}{3} + \ldots + \dfrac{1}{2n-1}...") |
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Latest revision as of 00:52, 9 August 2016
Theorem
The following formula holds for $n=1,2,3,\ldots$: $$\psi \left( n +\dfrac{1}{2} \right) = -\gamma - 2 \log(2)+ 2 \left( 1 + \dfrac{1}{3} + \ldots + \dfrac{1}{2n-1} \right),$$ where $\psi$ denotes the digamma function and $\gamma$ denotes the Euler-Mascheroni constant.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $6.3.4$
