DLMF:4.40.E7

MaRDI QIDQ2439

• Label: DLMF:4.40.E7

Digital Library of Mathematical Functions ID 4.40.E7

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

Constraint(s)

${\displaystyle{\displaystyle a\neq 0}}$

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
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\coth\NVar{z}}}$: hyperbolic cotangent function
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle a}}$: real or complex constant
• ${\displaystyle{\displaystyle x}}$: real variable
 

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