Formula:3135

Digital Library of Mathematical Functions ID 7.14.E5

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}C\left(t\right)\mathrm{d}t=\frac{1}{a}\mathrm{f}\left(\frac{a}{\pi}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\Re a>0}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}$: auxiliary function for Fresnel integrals
• ${\displaystyle{\displaystyle C\left(\NVar{z}\right)}}$: Fresnel integral
• ${\displaystyle{\displaystyle\pi}}$: 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
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
 

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