Difference between revisions of "Faddeeva function"
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(Created page with "The Faddeeva function is defined by $$w(z)=e^{-z^2} \left( 1 + \dfrac{2i}{\sqrt{\pi}} \displaystyle\int_0^x e^{t^2} dt \right)=e^{-z^2} \left[ 1 + \mathrm{erf}(iz)\right]=e^{-...") |
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| − | The Faddeeva function is defined by | + | The Faddeeva function (also called the Kramp function) is defined by |
$$w(z)=e^{-z^2} \left( 1 + \dfrac{2i}{\sqrt{\pi}} \displaystyle\int_0^x e^{t^2} dt \right)=e^{-z^2} \left[ 1 + \mathrm{erf}(iz)\right]=e^{-z^2} \mathrm{erfc}(-iz),$$ | $$w(z)=e^{-z^2} \left( 1 + \dfrac{2i}{\sqrt{\pi}} \displaystyle\int_0^x e^{t^2} dt \right)=e^{-z^2} \left[ 1 + \mathrm{erf}(iz)\right]=e^{-z^2} \mathrm{erfc}(-iz),$$ | ||
where $\mathrm{erf}$ denotes the [[error function]] and $\mathrm{erfc}$ denotes the [[complementary error function]]. | where $\mathrm{erf}$ denotes the [[error function]] and $\mathrm{erfc}$ denotes the [[complementary error function]]. | ||
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=References= | =References= | ||
[http://dualaud.net/specialfunctionswiki/abramowitz_and_stegun-1.03/page_297.htm] | [http://dualaud.net/specialfunctionswiki/abramowitz_and_stegun-1.03/page_297.htm] | ||
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| + | [[Category:SpecialFunction]] | ||
Latest revision as of 18:31, 24 May 2016
The Faddeeva function (also called the Kramp function) is defined by $$w(z)=e^{-z^2} \left( 1 + \dfrac{2i}{\sqrt{\pi}} \displaystyle\int_0^x e^{t^2} dt \right)=e^{-z^2} \left[ 1 + \mathrm{erf}(iz)\right]=e^{-z^2} \mathrm{erfc}(-iz),$$ where $\mathrm{erf}$ denotes the error function and $\mathrm{erfc}$ denotes the complementary error function.
