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DedekindEta




Mathematica Notation

Traditional Notation









Elliptic Functions > DedekindEta[z] > Differentiation > Low-order differentiation





http://functions.wolfram.com/09.49.20.0005.01









  


  








Input Form





Derivative[1][DedekindEta][I] == -((I Pi^(1/4))/(Sqrt[2] Gamma[-(1/4)]))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["DedekindEta", TagBox[RowBox[List["(", "1", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "\[ImaginaryI]", "]"]], "\[Equal]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[Pi]", RowBox[List["1", "/", "4"]]]]], RowBox[List[SqrtBox["2"], " ", RowBox[List["Gamma", "[", RowBox[List["-", FractionBox["1", "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> <msup> <mi> &#951; </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> &#8520; </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mroot> <mi> &#960; </mi> <mn> 4 </mn> </mroot> </mrow> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <imaginaryi /> </bvar> <apply> <ci> &#951; </ci> <imaginaryi /> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["DedekindEta", "\[Prime]", Rule[MultilineFunction, None]], "[", "\[ImaginaryI]", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[Pi]", RowBox[List["1", "/", "4"]]]]], RowBox[List[SqrtBox["2"], " ", RowBox[List["Gamma", "[", RowBox[List["-", FractionBox["1", "4"]]], "]"]]]]]]]]]]]


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





2007-05-02