Formula:2137

Digital Library of Mathematical Functions ID 4.26.E12

${\displaystyle{\displaystyle\int_{0}^{\infty}\frac{\sin\left(mt\right)}{t}\mathrm{d}t=\begin{cases}\frac{1}{2}\pi,&m>0,\\ 0,&m=0,\\ -\frac{1}{2}\pi,&m<0.\end{cases}}}$

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
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle m}}$: integer
 

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