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FresnelC






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > FresnelC[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function > Involving exp and power > Linear arguments





http://functions.wolfram.com/06.33.21.0021.01









  


  










Input Form





Integrate[z^3 E^(b z^2) FresnelC[a z], z] == (1/(8 b^2)) ((-((4 a b z)/(4 b^2 + a^4 Pi^2))) (2 b Cos[(1/2) a^2 Pi z^2] + a^2 Pi Sin[(1/2) a^2 Pi z^2]) Exp[b z^2] + ((Sqrt[Pi] a (3 b - I a^2 Pi))/(2 (b - (1/2) I a^2 Pi)^(3/2))) Erfi[Sqrt[b - (1/2) I a^2 Pi] z] + ((Sqrt[Pi] a (3 b + I a^2 Pi))/(2 (b + (1/2) I a^2 Pi)^(3/2))) Erfi[Sqrt[b + (1/2) I a^2 Pi] z] + 4 E^(b z^2) (-1 + b z^2) FresnelC[a z])










Standard Form





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MathML Form







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Rule Form





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





2001-10-29





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