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FresnelC






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > FresnelC[z] > Integration > Indefinite integration > Involving direct function and Gamma-, Beta-, Erf-type functions > Involving erf-type functions and a power function > Involving erfi and power





http://functions.wolfram.com/06.33.21.0126.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) Erfi[b z] FresnelC[a z], z] == (z^\[Alpha]/\[Alpha]) FresnelC[a z] (Erfi[b z] - (b z ((-b^2) z^2)^((1/2) (-1 - \[Alpha])) Gamma[(1 + \[Alpha])/2, 0, (-b^2) z^2])/Sqrt[Pi]) + 2 I a Sum[(((-1)^k 2^(-1 + k + \[Alpha]/2) (I b)^(1 + 2 k) Pi^(-k - (\[Alpha] + 3)/2) z^(2 + 2 k + \[Alpha]))/ ((1 + 2 k) (1 + 2 k + \[Alpha]) k!)) ((I a^2 z^2)^(-1 + k + \[Alpha]/2) (a^4 z^4)^(-k - \[Alpha]/2) Gamma[\[Alpha]/2 + k + 1, (-(1/2)) I a^2 Pi z^2] + ((-I) a^2 z^2)^(-1 + k + \[Alpha]/2) (a^4 z^4)^(-k - \[Alpha]/2) Gamma[\[Alpha]/2 + k + 1, (1/2) I a^2 Pi z^2]), {k, 0, Infinity}]










Standard Form





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MathML Form







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</ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> k </ci> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <imaginaryi /> <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> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29