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FresnelC




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > FresnelC[z] > Integration > Indefinite integration > Involving direct function and Gamma-, Beta-, Erf-type functions > Involving erf-type functions and a power function > Involving erfi and power





http://functions.wolfram.com/06.33.21.0127.01









  


  








Input Form





Integrate[z^2 Erfi[b z] FresnelC[a z], z] == (1/(12 Pi^2)) (((4 Pi^(3/2))/b^3) (E^(b^2 z^2) (1 - b^2 z^2) + b^3 Sqrt[Pi] z^3 Erfi[b z]) FresnelC[a z] + (2/(a^3 b^3)) (((4 b^4 + I a^2 b^2 Pi - a^4 Pi^2)/Sqrt[-2 I b^2 + a^2 Pi]) (FresnelC[Sqrt[a^2 - (2 I b^2)/Pi] z] + I FresnelS[Sqrt[a^2 - (2 I b^2)/Pi] z]) + ((4 b^4 - I a^2 b^2 Pi - a^4 Pi^2)/Sqrt[2 I b^2 + a^2 Pi]) (FresnelC[Sqrt[a^2 + (2 I b^2)/Pi] z] - I FresnelS[Sqrt[a^2 + (2 I b^2)/Pi] z])) + (4 Sqrt[Pi] z Cosh[b^2 z^2] Sin[(1/2) a^2 Pi z^2])/(a b) - (4 Erfi[b z] (2 Cos[(1/2) a^2 Pi z^2] + a^2 Pi z^2 Sin[(1/2) a^2 Pi z^2]))/ a^3 - ((Sqrt[Pi] z)/(a b)) (I Sqrt[2 Pi] (-(1/Sqrt[(-2 b^2 + I a^2 Pi) z^2]) + 1/Sqrt[(-(2 b^2 + I a^2 Pi)) z^2]) - 4 Sin[(1/2) a^2 Pi z^2] Sinh[b^2 z^2]))








Standard Form





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MathML Form







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<bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <ci> FresnelC </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <pi /> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <power /> 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29