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WeierstrassPPrime




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassPPrime[z,{g2,g3}] > Specific values > Specialized values > For fixed {g2,g3}





http://functions.wolfram.com/09.14.03.0006.01









  


  








Input Form





WeierstrassPPrime[m Subscript[\[Omega], 1] + n Subscript[\[Omega], 3], {Subscript[g, 2], Subscript[g, 3]}] == 0 /; Element[{(m - 1)/2, n}, Integers] || Element[{m, (n - 1)/2}, Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["WeierstrassPPrime", "[", RowBox[List[RowBox[List[RowBox[List["m", " ", SubscriptBox["\[Omega]", "1"]]], "+", RowBox[List["n", " ", SubscriptBox["\[Omega]", "3"]]]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["m", "-", "1"]], "2"], ",", "n"]], "}"]], "\[Element]", "Integers"]], "\[Or]", RowBox[List[RowBox[List["{", RowBox[List["m", ",", FractionBox[RowBox[List["n", "-", "1"]], "2"]]], "}"]], "\[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> <msup> <mi> &#8472; </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mrow> <mrow> <mrow> <mrow> <mi> m </mi> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mi> n </mi> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> { </mo> <mrow> <mfrac> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mi> n </mi> </mrow> <mo> } </mo> </mrow> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mi> m </mi> <mo> , </mo> <mfrac> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> } </mo> </mrow> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <ci> &#8472; </ci> </apply> <apply> <ci> CompoundExpression </ci> <apply> <plus /> <apply> <times /> <ci> m </ci> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <ci> n </ci> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <or /> <apply> <in /> <list> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> n </ci> </list> <integers /> </apply> <apply> <in /> <list> <ci> m </ci> <apply> <times /> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </list> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassPPrime", "[", RowBox[List[RowBox[List[RowBox[List["m_", " ", SubscriptBox["\[Omega]_", "1"]]], "+", RowBox[List["n_", " ", SubscriptBox["\[Omega]_", "3"]]]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["m", "-", "1"]], "2"], ",", "n"]], "}"]], "\[Element]", "Integers"]], "||", RowBox[List[RowBox[List["{", RowBox[List["m", ",", FractionBox[RowBox[List["n", "-", "1"]], "2"]]], "}"]], "\[Element]", "Integers"]]]]]]]]]]


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





2001-10-29