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FresnelS






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > FresnelS[z] > Integration > Indefinite integration > Involving one direct function and a power function > Linear arguments





http://functions.wolfram.com/06.32.21.0004.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) FresnelS[z], z] == (z^\[Alpha] FresnelS[z])/\[Alpha] + ((I/\[Alpha]) 2^((\[Alpha] - 3)/2) z^(1 + \[Alpha]) ((-(I z^2)^((1 + \[Alpha])/2)) Gamma[(1 + \[Alpha])/2, (-(1/2)) I Pi z^2] + ((-I) z^2)^((1 + \[Alpha])/2) Gamma[(1 + \[Alpha])/2, (1/2) I Pi z^2]))/(Pi^((\[Alpha] + 1)/2) (z^4)^((\[Alpha] + 1)/2))










Standard Form





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MathML Form







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</ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> &#945; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </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





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