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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/06.33.21.0016.01









  


  










Input Form





Integrate[z E^(b z) FresnelC[a z], z] == ((1/(2 a^2 b^2 Pi)) (I a b E^((I b^2)/(2 a^2 Pi) + b z) (-1 + E^(I a^2 Pi z^2)) + E^((1/2) I a^2 Pi z^2) (2 a^2 E^((I b^2)/(2 a^2 Pi) + b z) Pi (-1 + b z) FresnelC[a z] - (b^2 - I a^2 Pi) (FresnelC[b/(a Pi) - I a z] + I FresnelS[b/(a Pi) - I a z]) - E^((I b^2)/(a^2 Pi)) (b^2 + I a^2 Pi) (FresnelC[b/(a Pi) + I a z] - I FresnelS[b/(a Pi) + I a z]))))/ E^((I (b^2 + a^4 Pi^2 z^2))/(2 a^2 Pi))










Standard Form





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MathML Form







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type='integer'> 2 </cn> </apply> <pi /> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> FresnelC </ci> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <times /> <ci> a </ci> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <ci> FresnelS </ci> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <times /> <ci> a </ci> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





© 1998- Wolfram Research, Inc.