DLMF:7.20.E1 (Q2479)

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DLMF:7.20.E1
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    1 σ ⁢ 2 ⁢ π ⁢ ∫ - ∞ x e - ( t - m ) 2 / ( 2 ⁢ σ 2 ) ⁢ d t = 1 2 ⁢ erfc ⁡ ( m - x σ ⁢ 2 ) = Q ⁢ ( m - x σ ) = P ⁢ ( x - m σ ) . 1 𝜎 2 𝜋 superscript subscript 𝑥 superscript 𝑒 superscript 𝑡 𝑚 2 2 superscript 𝜎 2 𝑡 1 2 complementary-error-function 𝑚 𝑥 𝜎 2 𝑄 𝑚 𝑥 𝜎 𝑃 𝑥 𝑚 𝜎 {\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).}}
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    DLMF:7.20.E1
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