Formula:3072

Digital Library of Mathematical Functions ID 7.7.E4

${\displaystyle{\displaystyle\int_{0}^{\infty}\frac{e^{-at}}{\sqrt{t+z^{2}}}\mathrm{d}t=\sqrt{\frac{\pi}{a}}e^{az^{2}}\operatorname{erfc}\left(\sqrt{a}z\right),}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}$: complementary error function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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