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FresnelC




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > FresnelC[z] > Integration > Indefinite integration > Involving only one direct function





http://functions.wolfram.com/06.33.21.0003.01









  


  








Input Form





Integrate[FresnelC[z], z] == z FresnelC[z] - (1/Pi) Sin[(Pi z^2)/2]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["FresnelC", "[", "z", "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["z", " ", RowBox[List["FresnelC", "[", "z", "]"]]]], "-", RowBox[List[FractionBox["1", "\[Pi]"], RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", SuperscriptBox["z", "2"]]], "2"], "]"]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mrow> <semantics> <mi> C </mi> <annotation encoding='Mathematica'> TagBox[&quot;C&quot;, FresnelC] </annotation> </semantics> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <semantics> <mi> C </mi> <annotation encoding='Mathematica'> TagBox[&quot;C&quot;, FresnelC] </annotation> </semantics> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> &#960; </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <ci> FresnelC </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <ci> FresnelC </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["FresnelC", "[", "z_", "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["z", " ", RowBox[List["FresnelC", "[", "z", "]"]]]], "-", FractionBox[RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", SuperscriptBox["z", "2"]]], "2"], "]"]], "\[Pi]"]]]]]]]


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





2001-10-29