Formula:3166

Digital Library of Mathematical Functions ID 7.19.E4

${\displaystyle{\displaystyle H\left(a,u\right)=\frac{a}{\pi}\int_{-\infty}^{\infty}\frac{e^{-t^{2}}\mathrm{d}t}{(u-t)^{2}+a^{2}}=\frac{1}{a\sqrt{\pi}}\mathsf{U}\left(\frac{u}{a},\frac{1}{4a^{2}}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\mathsf{U}\left(\NVar{x},\NVar{t}\right)}}$: Voigt function
• ${\displaystyle{\displaystyle\pi}}$: 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
 

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