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Formula:3020

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Digital Library of Mathematical Functions ID 7.2.E2

erfc ⁡ z = 2 π ⁢ ∫ z ∞ e - t 2 ⁢ d t = 1 - erf ⁡ z , complementary-error-function 𝑧 2 𝜋 superscript subscript 𝑧 superscript 𝑒 superscript 𝑡 2 𝑡 1 error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}z=\frac{2}{\sqrt{\pi}}\int_{z}^% {\infty}e^{-t^{2}}\mathrm{d}t=1-\operatorname{erf}z,}}


Constraint(s)

Symbols List

  • π {\displaystyle{\displaystyle\pi}} : the ratio of the circumference of a circle to its diameter
  • d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}} : differential of x
  • erf ⁡ z error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}} : error function
  • e {\displaystyle{\displaystyle\mathrm{e}}} : base of natural logarithm
  • ∫ {\displaystyle{\displaystyle\int}} : integral
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
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