Formula:2649

Digital Library of Mathematical Functions ID 5.7.E8

${\displaystyle{\displaystyle\Im\psi\left(1+\mathrm{i}y\right)=\sum_{k=1}^{\infty}\frac{y}{k^{2}+y^{2}}.}}$

Symbols List

• ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$: psi (or digamma) function
• ${\displaystyle{\displaystyle\Im}}$: imaginary part
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle y}}$: real variable
 

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