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variants of this functions
WeierstrassSigma




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassSigma[n,z,{g2,g3}] > General characteristics > Domain and analyticity





http://functions.wolfram.com/09.16.04.0001.01









  


  








Input Form





DomainAndRange[Function[{z, Subscript[g, 2], Subscript[g, 3]}, WeierstrassSigma[n, z, {Subscript[g, 2], Subscript[g, 3]}]]] == PowerProduct[{1, 2, 3}, Complexes, ProductSet[Complexes, Complexes]] \[LongRightArrow] Complexes








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["z", ",", SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], ",", RowBox[List["WeierstrassSigma", "[", RowBox[List["n", ",", "z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "]"]], "]"]], " ", "\[Equal]", "\[IndentingNewLine]", RowBox[List[RowBox[List["PowerProduct", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]], ",", "Complexes", ",", RowBox[List["ProductSet", "[", RowBox[List["Complexes", ",", "Complexes"]], "]"]]]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]








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> <mo> ( </mo> <mrow> <mi> n </mi> <mo> * </mo> <mi> z </mi> <mo> * </mo> <mrow> <mo> { </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> * </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <semantics> <mrow> <msub> <mi> &#963; </mi> <mi> n </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubscriptBox[&quot;\[Sigma]&quot;, &quot;n&quot;], &quot;(&quot;, RowBox[List[&quot;z&quot;, &quot;,&quot;, SubscriptBox[&quot;g&quot;, &quot;2&quot;], &quot;,&quot;, SubscriptBox[&quot;g&quot;, &quot;3&quot;]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> </mrow> <mo> &#8759; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> } </mo> </mrow> <mo> &#8855; </mo> <mi> &#8450; </mi> <mo> &#8855; </mo> <mrow> <mo> { </mo> <mrow> <mi> &#8450; </mi> <mo> &#8855; </mo> <mi> &#8450; </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <mi> &#8450; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> * </mo> <mi> z </mi> <mo> * </mo> <mrow> <mo> { </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> * </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <semantics> <mrow> <msub> <mi> &#963; </mi> <mi> n </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubscriptBox[&quot;\[Sigma]&quot;, &quot;n&quot;], &quot;(&quot;, RowBox[List[&quot;z&quot;, &quot;,&quot;, SubscriptBox[&quot;g&quot;, &quot;2&quot;], &quot;,&quot;, SubscriptBox[&quot;g&quot;, &quot;3&quot;]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> </mrow> <mo> &#8759; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> } </mo> </mrow> <mo> &#8855; </mo> <mi> &#8450; </mi> <mo> &#8855; </mo> <mrow> <mo> { </mo> <mrow> <mi> &#8450; </mi> <mo> &#8855; </mo> <mi> &#8450; </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <mi> &#8450; </mi> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]], ",", RowBox[List["WeierstrassSigma", "[", RowBox[List["n_", ",", "z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["PowerProduct", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]], ",", "Complexes", ",", RowBox[List["ProductSet", "[", RowBox[List["Complexes", ",", "Complexes"]], "]"]]]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]


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





2001-10-29