DLMF:4.40.E8

MaRDI QIDQ2441

• Label: DLMF:4.40.E8

Digital Library of Mathematical Functions ID 4.40.E8

${\displaystyle{\displaystyle\int_{0}^{\infty}\frac{\sinh\left(ax\right)}{\sinh\left(\pi x\right)}\mathrm{d}x=\tfrac{1}{2}\tan\left(\tfrac{1}{2}a\right),}}$

Constraint(s)

${\displaystyle{\displaystyle-\pi<a<\pi}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\tan\NVar{z}}}$: tangent function
• ${\displaystyle{\displaystyle a}}$: real or complex constant
• ${\displaystyle{\displaystyle x}}$: real variable
 

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