Formula:1733

Digital Library of Mathematical Functions ID 4.10.E11

${\displaystyle{\displaystyle\int_{-\infty}^{\infty}e^{-cx^{2}}\mathrm{d}x=\sqrt{\frac{\pi}{c}},}}$

Constraint(s)

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

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
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle c}}$: real or complex constant
• ${\displaystyle{\displaystyle x}}$: real variable
 

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