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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 power, exponential and hyperbolic functions > Involving power, exp and cosh





http://functions.wolfram.com/06.33.21.0096.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) E^(b z) Cosh[c z] FresnelC[a z], z] == ((a z^\[Alpha])/2) Sum[(((-1)^k Pi^(2 k) a^(4 k))/ (2^(2 k) ((4 k + 1) (2 k)!))) (((b + c)^(-4 k - 1) Gamma[1 + 4 k + \[Alpha], (-(b + c)) z])/ ((-b - c) z)^\[Alpha] + ((b - c)^(-4 k - 1) Gamma[1 + 4 k + \[Alpha], (-(b - c)) z])/((-b + c) z)^\[Alpha]), {k, 0, Infinity}]










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