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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/06.33.21.0112.01









  


  








Input Form





Integrate[z FresnelC[a z]^2, z] == (-(1/(8 a^2 Pi^2))) (2 Cos[a^2 Pi z^2] - 2 a^2 Pi^2 z^2 FresnelC[a z]^2 + 4 a Pi z Cos[(1/2) a^2 Pi z^2] FresnelS[a z] + 2 a^2 Pi^2 z^2 FresnelS[a z]^2 - 2 a^4 Pi^2 z^4 HypergeometricPFQ[{1/2, 1}, {3/4, 5/4, 3/2}, (-(1/16)) a^4 Pi^2 z^4] + a^4 Pi^2 z^4 HypergeometricPFQ[{1, 1}, {3/4, 5/4, 2}, (-(1/16)) a^4 Pi^2 z^4] - 4 Pi FresnelC[a z] (FresnelS[a z] - a z Sin[(1/2) a^2 Pi z^2]))








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