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FresnelS




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > FresnelS[z] > Differentiation > Fractional integro-differentiation





http://functions.wolfram.com/06.32.20.0005.02









  


  








Input Form





D[FresnelS[z], {z, \[Alpha]}] == 2^(2 \[Alpha] - 11/2) Pi^(5/2) z^(3 - \[Alpha]) HypergeometricPFQRegularized[{3/4, 1, 5/4}, {1 - \[Alpha]/4, (5 - \[Alpha])/4, (6 - \[Alpha])/4, (7 - \[Alpha])/4}, -((Pi^2 z^4)/16)]








Standard Form





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MathML Form







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</mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mfrac> <mn> 5 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mi> &#945; </mi> <mn> 4 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mrow> <mn> 5 </mn> <mo> - </mo> <mi> &#945; </mi> </mrow> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mn> 6 </mn> <mo> - </mo> <mi> &#945; </mi> </mrow> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mn> 7 </mn> <mo> - </mo> <mi> &#945; </mi> </mrow> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <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> 16 </mn> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;3&quot;, TraditionalForm]], SubscriptBox[OverscriptBox[&quot;F&quot;, &quot;~&quot;], FormBox[&quot;4&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;3&quot;, &quot;4&quot;], HypergeometricPFQRegularized, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;1&quot;, HypergeometricPFQRegularized, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;5&quot;, &quot;4&quot;], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, FractionBox[&quot;\[Alpha]&quot;, &quot;4&quot;]]], HypergeometricPFQRegularized, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;5&quot;, &quot;-&quot;, &quot;\[Alpha]&quot;]], &quot;4&quot;], HypergeometricPFQRegularized, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;6&quot;, &quot;-&quot;, &quot;\[Alpha]&quot;]], &quot;4&quot;], HypergeometricPFQRegularized, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;7&quot;, &quot;-&quot;, &quot;\[Alpha]&quot;]], &quot;4&quot;], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[&quot;-&quot;, FractionBox[RowBox[List[SuperscriptBox[&quot;\[Pi]&quot;, &quot;2&quot;], &quot; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["FresnelS", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["2", " ", "\[Alpha]"]], "-", FractionBox["11", "2"]]]], " ", SuperscriptBox["\[Pi]", RowBox[List["5", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "-", "\[Alpha]"]]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", "1", ",", FractionBox["5", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox["\[Alpha]", "4"]]], ",", FractionBox[RowBox[List["5", "-", "\[Alpha]"]], "4"], ",", FractionBox[RowBox[List["6", "-", "\[Alpha]"]], "4"], ",", FractionBox[RowBox[List["7", "-", "\[Alpha]"]], "4"]]], "}"]], ",", RowBox[List[RowBox[List["-", FractionBox["1", "16"]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "4"]]], ")"]]]]]], "]"]]]]]]]]


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





2001-10-29