Formula:2595

Digital Library of Mathematical Functions ID 5.4.E19

${\displaystyle{\displaystyle\psi\left(\frac{p}{q}\right)=-\gamma-\ln q-\frac{\pi}{2}\cot\left(\frac{\pi p}{q}\right)+\frac{1}{2}\sum_{k=1}^{q-1}\cos\left(\frac{2\pi kp}{q}\right)\ln\left(2-2\cos\left(\frac{2\pi k}{q}\right)\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\gamma}}$: Euler’s constant
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\cot\NVar{z}}}$: cotangent function
• ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$: psi (or digamma) function
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle q}}$: real or complex variable
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
 

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