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JacobiSC




Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiSC[z,m] > Specific values > Specialized values > For fixed z > Case m=1





http://functions.wolfram.com/09.34.03.0031.01









  


  








Input Form





JacobiSC[z + (Pi k I)/2, 1] == Sinh[z + (k Pi I)/2] /; Element[k, Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["JacobiSC", "[", RowBox[List[RowBox[List["z", "+", FractionBox[RowBox[List["\[Pi]", " ", "k", " ", "\[ImaginaryI]"]], "2"]]], ",", "1"]], "]"]], "\[Equal]", RowBox[List["Sinh", "[", RowBox[List["z", "+", FractionBox[RowBox[List["k", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "2"]]], "]"]]]], "/;", RowBox[List["k", "\[Element]", "Integers"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> sc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> &#10072; </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[List[], Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> JacobiSC </ci> <apply> <plus /> <ci> z </ci> <apply> <times /> <imaginaryi /> <pi /> <ci> k </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <sinh /> <apply> <plus /> <ci> z </ci> <apply> <times /> <imaginaryi /> <pi /> <ci> k </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> k </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiSC", "[", RowBox[List[RowBox[List["z_", "+", FractionBox[RowBox[List["\[Pi]", " ", "k", " ", "\[ImaginaryI]"]], "2"]]], ",", "1"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Sinh", "[", RowBox[List["z", "+", FractionBox[RowBox[List["k", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "2"]]], "]"]], "/;", RowBox[List["k", "\[Element]", "Integers"]]]]]]]]


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





2007-05-02