Formula:3075

Digital Library of Mathematical Functions ID 7.7.E7

${\displaystyle{\displaystyle\int_{x}^{\infty}e^{-a^{2}t^{2}-(b^{2}/t^{2})}\mathrm{d}t=\frac{\sqrt{\pi}}{4a}\left(e^{2ab}\operatorname{erfc}\left(ax+(b/x)\right)+e^{-2ab}\operatorname{erfc}\left(ax-(b/x)\right)\right),}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}a|<\tfrac{1}{4}\pi}}$
${\displaystyle{\displaystyle x>0}}$
${\displaystyle{\displaystyle|\operatorname{ph}a|<\tfrac{1}{4}\pi}}$

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
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle x}}$: real variable
 

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