Formula:4176

Digital Library of Mathematical Functions ID 10.24.E3

${\displaystyle{\displaystyle\Gamma\left(1+i\nu\right)=\left(\frac{\pi\nu}{\sinh\left(\pi\nu\right)}\right)^{\frac{1}{2}}e^{i\gamma_{\nu}},}}$

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
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
• ${\displaystyle{\displaystyle\gamma_{\nu}}}$: parameter
 

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