![](/common/images/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
http://functions.wolfram.com/09.57.04.0001.01
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
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
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
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"]]]]]]
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
<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> ⋆ </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> ⋆ </mo> <mrow> <mo> { </mo> <mrow> <mi> a </mi> <mo> ⋆ </mo> <mi> b </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⟶ </mo> <semantics> <mrow> <mi> elog </mi> <mo> ⁡ </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["elog", "(", RowBox[List[SubscriptBox["z", "1"], ",", RowBox[List[SubscriptBox["z", "2"], ";", "a"]], ",", "b"]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> </mrow> <mo> ∷ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mi> ℂ </mi> <mo> ⊗ </mo> <mi> ℂ </mi> </mrow> <mo> } </mo> </mrow> <mo> ⊗ </mo> <mrow> <mo> { </mo> <mrow> <mi> ℂ </mi> <mo> ⊗ </mo> <mi> ℂ </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⟶ </mo> <mi> ℂ </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> ⋆ </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> ⋆ </mo> <mrow> <mo> { </mo> <mrow> <mi> a </mi> <mo> ⋆ </mo> <mi> b </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⟶ </mo> <semantics> <mrow> <mi> elog </mi> <mo> ⁡ </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["elog", "(", RowBox[List[SubscriptBox["z", "1"], ",", RowBox[List[SubscriptBox["z", "2"], ";", "a"]], ",", "b"]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> </mrow> <mo> ∷ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mi> ℂ </mi> <mo> ⊗ </mo> <mi> ℂ </mi> </mrow> <mo> } </mo> </mrow> <mo> ⊗ </mo> <mrow> <mo> { </mo> <mrow> <mi> ℂ </mi> <mo> ⊗ </mo> <mi> ℂ </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⟶ </mo> <mi> ℂ </mi> </mrow> </mrow> </annotation-xml> </semantics> </math>
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/clear.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| | ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| 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"]]]]]] |
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
Date Added to functions.wolfram.com (modification date)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/common/images/spacer.gif) |
|
|