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EllipticLog




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticLog[{z1,z2},{a,b}] > General characteristics > Domain and analyticity





http://functions.wolfram.com/09.57.04.0001.01









  


  








Input Form





DomainAndRange[Function[{{Subscript[z, 1], Subscript[z, 2]}, {a, b}}, EllipticLog[{Subscript[z, 1], Subscript[z, 2]}, {a, b}]]] == PowerProduct[ProductSet[Complexes, Complexes], ProductSet[Complexes, Complexes]] \[LongRightArrow] Complexes








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["a", ",", "b"]], "}"]]]], "}"]], ",", RowBox[List["EllipticLog", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["a", ",", "b"]], "}"]]]], "]"]]]], "]"]], "]"]], " ", "\[Equal]", "\[IndentingNewLine]", RowBox[List[RowBox[List["PowerProduct", "[", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["Complexes", ",", "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> <mrow> <mo> { </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> &#8902; </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> &#8902; </mo> <mrow> <mo> { </mo> <mrow> <mi> a </mi> <mo> &#8902; </mo> <mi> b </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <semantics> <mrow> <mi> elog </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <mi> a </mi> </mrow> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;elog&quot;, &quot;(&quot;, RowBox[List[SubscriptBox[&quot;z&quot;, &quot;1&quot;], &quot;,&quot;, RowBox[List[SubscriptBox[&quot;z&quot;, &quot;2&quot;], &quot;;&quot;, &quot;a&quot;]], &quot;,&quot;, &quot;b&quot;]], &quot;)&quot;]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> </mrow> <mo> &#8759; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mi> &#8450; </mi> <mo> &#8855; </mo> <mi> &#8450; </mi> </mrow> <mo> } </mo> </mrow> <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> <mrow> <mo> { </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> &#8902; </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> &#8902; </mo> <mrow> <mo> { </mo> <mrow> <mi> a </mi> <mo> &#8902; </mo> <mi> b </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <semantics> <mrow> <mi> elog </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <mi> a </mi> </mrow> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;elog&quot;, &quot;(&quot;, RowBox[List[SubscriptBox[&quot;z&quot;, &quot;1&quot;], &quot;,&quot;, RowBox[List[SubscriptBox[&quot;z&quot;, &quot;2&quot;], &quot;;&quot;, &quot;a&quot;]], &quot;,&quot;, &quot;b&quot;]], &quot;)&quot;]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> </mrow> <mo> &#8759; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mi> &#8450; </mi> <mo> &#8855; </mo> <mi> &#8450; </mi> </mrow> <mo> } </mo> </mrow> <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[RowBox[List["{", RowBox[List[SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["a_", ",", "b_"]], "}"]]]], "}"]], ",", RowBox[List["EllipticLog", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["a_", ",", "b_"]], "}"]]]], "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["PowerProduct", "[", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["Complexes", ",", "Complexes"]], "]"]], ",", RowBox[List["ProductSet", "[", RowBox[List["Complexes", ",", "Complexes"]], "]"]]]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]


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





2001-10-29