Formula:2561

Digital Library of Mathematical Functions ID 5.4.E4

${\displaystyle{\displaystyle\Gamma\left(\tfrac{1}{2}+\mathrm{i}y\right)\Gamma\left(\tfrac{1}{2}-\mathrm{i}y\right)=\left|\Gamma\left(\tfrac{1}{2}+\mathrm{i}y\right)\right|^{2}=\frac{\pi}{\cosh\left(\pi y\right)},}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle y}}$: real variable
 

Resources that cite this formula

No records found.