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FresnelC




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > FresnelC[z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself





http://functions.wolfram.com/06.33.06.0016.01









  


  








Input Form





FresnelC[z] \[Proportional] z (1 - (Pi^2 z^4)/40 + (Pi^4 z^8)/3456 - O[z^12])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["FresnelC", "[", "z", "]"]], "\[Proportional]", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "4"]]], "40"], "+", FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["z", "8"]]], "3456"], "-", RowBox[List["O", "[", SuperscriptBox["z", "12"], "]"]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <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> &#8733; </mo> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mrow> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mn> 40 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <msup> <mi> &#960; </mi> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mn> 3456 </mn> </mfrac> <mo> - </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> FresnelC </ci> <ci> z </ci> </apply> <apply> <times /> <ci> z </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <cn type='integer'> 40 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> <apply> <power /> <cn type='integer'> 3456 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> O </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 12 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FresnelC", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "4"]]], "40"], "+", FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["z", "8"]]], "3456"], "-", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "12"]]], ")"]]]]]]]]


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





2007-05-02