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FresnelC






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > FresnelC[z] > Representations through more general functions > Through Meijer G > Classical cases for the direct function itself





http://functions.wolfram.com/06.33.26.0003.01









  


  










Input Form





FresnelC[z] == ((Pi z^(3/4))/(Sqrt[2] (z^2)^(1/4) (-z)^(1/4))) MeijerG[{{}, {1}}, {{1/4}, {3/4, 0}}, (-(Pi^2/16)) z^4]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["FresnelC", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[RowBox[List["\[Pi]", " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]], " "]], RowBox[List[" ", RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "2"], ")"]], RowBox[List["1", "/", "4"]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "1", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "4"], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", "0"]], "}"]]]], "}"]], ",", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["\[Pi]", "2"], "16"]]], 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[&quot;C&quot;, FresnelC] </annotation> </semantics> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mrow> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mroot> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mn> 4 </mn> </mroot> <mo> &#8290; </mo> <mroot> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> </mrow> </mfrac> <mo> &#8290; </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mn> 16 </mn> </mfrac> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mn> 1 </mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mn> 0 </mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;3&quot;]], RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;0&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[RowBox[List[&quot;-&quot;, FractionBox[SuperscriptBox[&quot;\[Pi]&quot;, &quot;2&quot;], &quot;16&quot;]]], SuperscriptBox[&quot;z&quot;, &quot;4&quot;]]], MeijerG, Rule[Editable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[TagBox[&quot;1&quot;, MeijerG, Rule[Editable, True]]], List[RowBox[List[TagBox[FractionBox[&quot;1&quot;, &quot;4&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;3&quot;, &quot;4&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> FresnelC </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <pi /> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> MeijerG </ci> <list> <list /> <list> <cn type='integer'> 1 </cn> </list> </list> <list> <list> <cn type='rational'> 1 <sep /> 4 </cn> </list> <list> <cn type='rational'> 3 <sep /> 4 </cn> <cn type='integer'> 0 </cn> </list> </list> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 16 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <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]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[Pi]", " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "1", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "4"], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", "0"]], "}"]]]], "}"]], ",", RowBox[List[FractionBox["1", "16"], " ", RowBox[List["(", RowBox[List["-", SuperscriptBox["\[Pi]", "2"]]], ")"]], " ", SuperscriptBox["z", "4"]]]]], "]"]]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "2"], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]]










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





2001-10-29