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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 trigonometric functions > Involving power, exp and cos





http://functions.wolfram.com/06.33.21.0058.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) E^(b z) Cos[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 - I c)^(-4 k - 1) Gamma[1 + 4 k + \[Alpha], (-(b - I c)) z])/ ((-b + I c) z)^\[Alpha] + ((b + I c)^(-4 k - 1) Gamma[1 + 4 k + \[Alpha], (-(b + I c)) z])/((-b - I c) z)^\[Alpha]), {k, 0, Infinity}]










Standard Form





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MathML Form







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Rule Form





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2001-10-29





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