Formula:3073

Digital Library of Mathematical Functions ID 7.7.E5

${\displaystyle{\displaystyle\int_{0}^{1}\frac{e^{-at^{2}}}{t^{2}+1}\mathrm{d}t=\frac{\pi}{4}e^{a}\left(1-(\operatorname{erf}\sqrt{a})^{2}\right),}}$

Constraint(s)

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

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
• ${\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}$: error function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
 

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