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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 hyperbolic functions and a power function > Involving sinh and power





http://functions.wolfram.com/06.33.21.0073.01









  


  










Input Form





Integrate[z^3 Sinh[b z] FresnelC[a z], z] == (1/(2 a^6 b^4 Pi^3)) (I (FresnelC[(I b)/(a Pi) - a z] ((-b^2) (b^4 - 3 a^4 Pi^2) Cos[b^2/(2 a^2 Pi)] - 6 a^6 Pi^3 Sin[b^2/(2 a^2 Pi)]) + FresnelC[(I b)/(a Pi) + a z] ((-b^2) (b^4 - 3 a^4 Pi^2) Cos[b^2/(2 a^2 Pi)] - 6 a^6 Pi^3 Sin[b^2/(2 a^2 Pi)]) - (FresnelS[(I b)/(a Pi) - a z] + FresnelS[(I b)/(a Pi) + a z]) (6 a^6 Pi^3 Cos[b^2/(2 a^2 Pi)] - b^2 (b^4 - 3 a^4 Pi^2) Sin[b^2/(2 a^2 Pi)]) + 2 I a^3 b^3 Pi Cos[(1/2) a^2 Pi z^2] (-Cosh[b z] + b z Sinh[b z]) - 2 I a b Sin[(1/2) a^2 Pi z^2] ((b^4 - 6 a^4 Pi^2 - a^4 b^2 Pi^2 z^2) Cosh[b z] + 3 a^4 b Pi^2 z Sinh[b z]) - 2 I a^6 Pi^3 FresnelC[a z] (b z (6 + b^2 z^2) Cosh[b z] - 3 (2 + b^2 z^2) Sinh[b z])))










Standard Form





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MathML Form







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</mi> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <msup> <mi> b </mi> <mn> 4 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; 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Rule Form





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





2001-10-29