Difference between revisions of "Faddeeva function"

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The Faddeeva function is defined by
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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.

References

[1]