Formula:2629

Digital Library of Mathematical Functions ID 5.6.E7

${\displaystyle{\displaystyle|\Gamma\left(x+\mathrm{i}y\right)|\geq(\operatorname{sech}\left(\pi y\right))^{1/2}\Gamma\left(x\right),}}$

Constraint(s)

${\displaystyle{\displaystyle x\geq\tfrac{1}{2}}}$

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
• ${\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}$: hyperbolic secant function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle y}}$: real variable
 

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