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JacobiNC




Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiNC[z,m] > Specific values > Specialized values > For fixed m > Values at half-quarter-period points





http://functions.wolfram.com/09.31.03.0023.01









  


  








Input Form





JacobiNC[EllipticK[m]/2, m] == Sqrt[1 + Sqrt[1 - m]]/(1 - m)^(1/4)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["JacobiNC", "[", RowBox[List[FractionBox[RowBox[List["EllipticK", "[", "m", "]"]], "2"], ",", "m"]], "]"]], "\[Equal]", FractionBox[SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "m"]]]]]], RadicalBox[RowBox[List["1", "-", "m"]], "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> <mi> nc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </mfrac> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> </msqrt> </mrow> </msqrt> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> <mn> 4 </mn> </mroot> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiNC </ci> <apply> <times /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> m </ci> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiNC", "[", RowBox[List[FractionBox[RowBox[List["EllipticK", "[", "m_", "]"]], "2"], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "m"]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "m"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]


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





2001-10-29