|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/09.17.23.0001.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Sum[WeierstrassP[(2 k Subscript[\[Omega], 1])/n,
{Subscript[g, 2], Subscript[g, 3]}], {k, 1, n - 1}] ==
(n/Subscript[\[Omega], 1]) (WeierstrassZeta[Subscript[\[Omega], 1]/n,
WeierstrassInvariants[{Subscript[\[Omega], 1]/n,
Subscript[\[Omega], 3]}]] - Subscript[\[Eta], 1])
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], RowBox[List["n", "-", "1"]]], RowBox[List["WeierstrassP", "[", RowBox[List[FractionBox[RowBox[List["2", "k", " ", SubscriptBox["\[Omega]", "1"]]], "n"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "\[Equal]", RowBox[List[FractionBox["n", SubscriptBox["\[Omega]", "1"]], RowBox[List["(", RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List[FractionBox[SubscriptBox["\[Omega]", "1"], "n"], ",", RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List[FractionBox[SubscriptBox["\[Omega]", "1"], "n"], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "]"]]]], "]"]], "-", SubscriptBox["\[Eta]", "1"]]], ")"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mi> ℘ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> <mi> n </mi> </mfrac> <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> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mi> n </mi> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mfrac> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> <mi> n </mi> </mfrac> <mo> ; </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mfrac> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> <mi> n </mi> </mfrac> <mo> , </mo> <msub> <mi> ω </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mfrac> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> <mi> n </mi> </mfrac> <mo> , </mo> <msub> <mi> ω </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", RowBox[List[RowBox[List[TagBox[FractionBox[SubscriptBox["\[Omega]", "1"], "n"], Rule[Editable, True]], ";", TagBox[RowBox[List[SubscriptBox["g", "2"], "(", RowBox[List[FractionBox[SubscriptBox["\[Omega]", "1"], "n"], ",", SubscriptBox["\[Omega]", "3"]]], ")"]], Rule[Editable, True]]]], ",", TagBox[RowBox[List[SubscriptBox["g", "3"], "(", RowBox[List[FractionBox[SubscriptBox["\[Omega]", "1"], "n"], ",", SubscriptBox["\[Omega]", "3"]]], ")"]], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> - </mo> <msub> <mi> η </mi> <mn> 1 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <ci> WeierstrassP </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <list> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> </apply> <apply> <times /> <apply> <times /> <ci> n </ci> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <ci> WeierstrassZeta </ci> <apply> <times /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <list> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> </apply> </list> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> η </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], RowBox[List["n_", "-", "1"]]], RowBox[List["WeierstrassP", "[", RowBox[List[FractionBox[RowBox[List["2", " ", "k", " ", SubscriptBox["\[Omega]_", "1"]]], "n_"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["n", " ", RowBox[List["(", RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List[FractionBox[SubscriptBox["\[Omega]\[Omega]", "1"], "n"], ",", RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List[FractionBox[SubscriptBox["\[Omega]\[Omega]", "1"], "n"], ",", SubscriptBox["\[Omega]\[Omega]", "3"]]], "}"]], "]"]]]], "]"]], "-", SubscriptBox["\[Eta]", "1"]]], ")"]]]], SubscriptBox["\[Omega]\[Omega]", "1"]]]]]] |
|
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
){kind=small}
