Formula:3177

Digital Library of Mathematical Functions ID 7.20.E1

${\displaystyle{\displaystyle\frac{1}{\sigma\sqrt{2\pi}}\int_{-\infty}^{x}e^{-(t-m)^{2}/(2\sigma^{2})}\mathrm{d}t=\frac{1}{2}\operatorname{erfc}\left(\frac{m-x}{\sigma\sqrt{2}}\right)=Q\left(\frac{m-x}{\sigma}\right)=P\left(\frac{x-m}{\sigma}\right).}}$

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
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle m}}$: mean
• ${\displaystyle{\displaystyle\sigma}}$: standard deviation
 

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