Fresnel integral C: Series representations (formula 06.33.06.0004)

FresnelC

$Mathematica Notation$

Gamma, Beta, Erf

FresnelC[z]

Series representations

Generalized power series

Expansions at z==0

For the function itself

http://functions.wolfram.com/06.33.06.0004.02

Input Form

FresnelC[z] \[Proportional] z (1 + O[z^4])

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["FresnelC", "[", "z", "]"]], "\[Proportional]", RowBox[List["z", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", SuperscriptBox["z", "4"], "]"]]]], ")"]]]]]]]]

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["C", FresnelC] </annotation> </semantics> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <msup> <mi> z </mi> <mn> 4 </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> <ci> O </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </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", "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "4"]]], ")"]]]]]]]]

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

2001-10-29