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FresnelC




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > FresnelC[z] > Integration > Indefinite integration > Involving functions of the direct function and elementary functions > Involving elementary functions of the direct function and elementary functions > Involving powers of the direct function and a power function > Linear arguments





http://functions.wolfram.com/06.33.21.0114.01









  


  








Input Form





Integrate[z^3 FresnelC[a z]^2, z] == (-(1/(24 a^4 Pi^3))) (3 a^2 Pi z^2 Cos[a^2 Pi z^2] - 3 Pi (3 + a^4 Pi^2 z^4) FresnelC[a z]^2 + 3 Pi (3 + a^4 Pi^2 z^4) FresnelS[a z]^2 - 3 a^6 Pi^3 z^6 HypergeometricPFQ[{1/2, 1}, {3/4, 5/4, 3/2}, (-(1/16)) a^4 Pi^2 z^4] + a^6 Pi^3 z^6 HypergeometricPFQ[{1, 3/2}, {3/4, 5/4, 5/2}, (-(1/16)) a^4 Pi^2 z^4] + 6 a Pi z FresnelS[a z] (a^2 Pi z^2 Cos[(1/2) a^2 Pi z^2] - 3 Sin[(1/2) a^2 Pi z^2]) + 6 a Pi z FresnelC[a z] (3 Cos[(1/2) a^2 Pi z^2] + a^2 Pi z^2 Sin[(1/2) a^2 Pi z^2]) - 12 Sin[a^2 Pi z^2])








Standard Form





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MathML Form







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<times /> <cn type='integer'> 3 </cn> <apply> <cos /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <ci> a </ci> <pi /> <apply> <ci> FresnelS </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <cos /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <sin /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <pi /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> FresnelC </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <pi /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> FresnelS </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <sin /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </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