Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











WeierstrassP






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassP[z,{g2,g3}] > Transformations > Determinants involving derivatives





http://functions.wolfram.com/09.13.16.0021.01









  


  










Input Form





Det[Table[If[j == 0, 1, Derivative[j - 1, 0][WeierstrassP][Subscript[z, i], {Subscript[g, 2], Subscript[g, 3]}]], {i, 0, n}, {j, 0, n}]] == (-1)^n WeierstrassSigma[Sum[Subscript[z, i], {i, 0, n}], {Subscript[g, 2], Subscript[g, 3]}] Product[k!/WeierstrassSigma[Subscript[z, k], {Subscript[g, 2], Subscript[g, 3]}]^(n + 1), {k, 0, n}] Product[WeierstrassSigma[Subscript[z, j] - Subscript[z, i], {Subscript[g, 2], Subscript[g, 3]}], {i, 1, n - 1}, {j, i + 1, n}] /; Element[n, Integers] && n > 0










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Det", "[", RowBox[List["Table", "[", RowBox[List[RowBox[List["If", "[", RowBox[List[RowBox[List["j", "\[Equal]", "0"]], ",", "1", ",", RowBox[List[SuperscriptBox["WeierstrassP", TagBox[RowBox[List["(", RowBox[List[RowBox[List["j", "-", "1"]], ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List[SubscriptBox["z", "i"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "]"]], ",", RowBox[List["{", RowBox[List["i", ",", "0", ",", "n"]], "}"]], ",", RowBox[List["{", RowBox[List["j", ",", "0", ",", "n"]], "}"]]]], "]"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], SubscriptBox["z", "i"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], " ", RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List["k", "!"]], SuperscriptBox[RowBox[List["WeierstrassSigma", "[", RowBox[List[SubscriptBox["z", "k"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], RowBox[List["n", "+", "1"]]]]]], " ", ")"]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["i", "=", "1"]], RowBox[List["n", "-", "1"]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", RowBox[List["i", "+", "1"]]]], "n"], RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List[SubscriptBox["z", "j"], "-", SubscriptBox["z", "i"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mn> 1 </mn> </mtd> <mtd> <mrow> <mi> &#8472; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <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> </mtd> <mtd> <mrow> <msup> <mi> &#8472; </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <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> </mtd> <mtd> <mo> &#8230; </mo> </mtd> <mtd> <mrow> <msup> <mi> &#8472; </mi> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <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> </mtd> </mtr> <mtr> <mtd> <mn> 1 </mn> </mtd> <mtd> <mrow> <mi> &#8472; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <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> </mtd> <mtd> <mrow> <msup> <mi> &#8472; </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <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> </mtd> <mtd> <mo> &#8230; </mo> </mtd> <mtd> <mrow> <msup> <mi> &#8472; </mi> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <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> </mtd> </mtr> <mtr> <mtd> <mo> &#8942; </mo> </mtd> <mtd> <mo> &#8942; </mo> </mtd> <mtd> <mo> &#8942; </mo> </mtd> <mtd> <mo> &#8945; </mo> </mtd> <mtd> <mo> &#8942; </mo> </mtd> </mtr> <mtr> <mtd> <mn> 1 </mn> </mtd> <mtd> <mrow> <mi> &#8472; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mi> n </mi> </msub> <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> </mtd> <mtd> <mrow> <msup> <mi> &#8472; </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mi> n </mi> </msub> <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> </mtd> <mtd> <mo> &#8230; </mo> </mtd> <mtd> <mrow> <msup> <mi> &#8472; </mi> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mi> n </mi> </msub> <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> </mtd> </mtr> </mtable> <mo> &#10072; </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[LeftBracketingBar]&quot;, GridBox[List[List[&quot;1&quot;, RowBox[List[&quot;\[WeierstrassP]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;0&quot;], &quot;;&quot;, SubscriptBox[&quot;g&quot;, &quot;2&quot;]]], &quot;,&quot;, SubscriptBox[&quot;g&quot;, &quot;3&quot;]]], &quot;)&quot;]], RowBox[List[SuperscriptBox[&quot;\[WeierstrassP]&quot;, &quot;\[Prime]&quot;], &quot;(&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;0&quot;], &quot;;&quot;, SubscriptBox[&quot;g&quot;, &quot;2&quot;]]], &quot;,&quot;, SubscriptBox[&quot;g&quot;, &quot;3&quot;]]], &quot;)&quot;]], &quot;\[Ellipsis]&quot;, RowBox[List[SuperscriptBox[&quot;\[WeierstrassP]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;n&quot;, &quot;-&quot;, &quot;1&quot;]], &quot;)&quot;]]], &quot;(&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;0&quot;], &quot;;&quot;, SubscriptBox[&quot;g&quot;, &quot;2&quot;]]], &quot;,&quot;, SubscriptBox[&quot;g&quot;, &quot;3&quot;]]], &quot;)&quot;]]], List[&quot;1&quot;, RowBox[List[&quot;\[WeierstrassP]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;1&quot;], &quot;;&quot;, SubscriptBox[&quot;g&quot;, &quot;2&quot;]]], &quot;,&quot;, SubscriptBox[&quot;g&quot;, &quot;3&quot;]]], &quot;)&quot;]], RowBox[List[SuperscriptBox[&quot;\[WeierstrassP]&quot;, &quot;\[Prime]&quot;], &quot;(&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;1&quot;], &quot;;&quot;, SubscriptBox[&quot;g&quot;, &quot;2&quot;]]], &quot;,&quot;, SubscriptBox[&quot;g&quot;, &quot;3&quot;]]], &quot;)&quot;]], &quot;\[Ellipsis]&quot;, RowBox[List[SuperscriptBox[&quot;\[WeierstrassP]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;n&quot;, &quot;-&quot;, &quot;1&quot;]], &quot;)&quot;]]], &quot;(&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;1&quot;], &quot;;&quot;, SubscriptBox[&quot;g&quot;, &quot;2&quot;]]], &quot;,&quot;, SubscriptBox[&quot;g&quot;, &quot;3&quot;]]], &quot;)&quot;]]], List[&quot;\[VerticalEllipsis]&quot;, &quot;\[VerticalEllipsis]&quot;, &quot;\[VerticalEllipsis]&quot;, &quot;\[DescendingEllipsis]&quot;, &quot;\[VerticalEllipsis]&quot;], List[&quot;1&quot;, RowBox[List[&quot;\[WeierstrassP]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;n&quot;], &quot;;&quot;, SubscriptBox[&quot;g&quot;, &quot;2&quot;]]], &quot;,&quot;, SubscriptBox[&quot;g&quot;, &quot;3&quot;]]], &quot;)&quot;]], RowBox[List[SuperscriptBox[&quot;\[WeierstrassP]&quot;, &quot;\[Prime]&quot;], &quot;(&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;n&quot;], &quot;;&quot;, SubscriptBox[&quot;g&quot;, &quot;2&quot;]]], &quot;,&quot;, SubscriptBox[&quot;g&quot;, &quot;3&quot;]]], &quot;)&quot;]], &quot;\[Ellipsis]&quot;, RowBox[List[SuperscriptBox[&quot;\[WeierstrassP]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;n&quot;, &quot;-&quot;, &quot;1&quot;]], &quot;)&quot;]]], &quot;(&quot;, RowBox[List[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;n&quot;], &quot;;&quot;, SubscriptBox[&quot;g&quot;, &quot;2&quot;]]], &quot;,&quot;, SubscriptBox[&quot;g&quot;, &quot;3&quot;]]], &quot;)&quot;]]]]], &quot;\[RightBracketingBar]&quot;]], List[Det]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#963; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> i </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <msub> <mi> z </mi> <mi> i </mi> </msub> </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> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Sigma]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[TagBox[RowBox[List[UnderoverscriptBox[&quot;\[Sum]&quot;, RowBox[List[&quot;i&quot;, &quot;=&quot;, &quot;0&quot;]], &quot;n&quot;], SubscriptBox[&quot;z&quot;, &quot;i&quot;]]], Rule[Editable, True]], &quot;;&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], Rule[Editable, True]]]], &quot;,&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mfrac> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> <msup> <semantics> <mrow> <mi> &#963; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mi> k </mi> </msub> <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> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Sigma]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[TagBox[SubscriptBox[&quot;z&quot;, &quot;k&quot;], Rule[Editable, True]], &quot;;&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], Rule[Editable, True]]]], &quot;,&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> i </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mrow> <mi> i </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mi> n </mi> </munderover> <semantics> <mrow> <mi> &#963; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> z </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> z </mi> <mi> i </mi> </msub> </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> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Sigma]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[TagBox[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;j&quot;], &quot;-&quot;, SubscriptBox[&quot;z&quot;, &quot;i&quot;]]], Rule[Editable, True]], &quot;;&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], Rule[Editable, True]]]], &quot;,&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <determinant /> <list> <list> <cn type='integer'> 1 </cn> <apply> <ci> WeierstrassP </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </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> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <ci> &#8472; </ci> </apply> <apply> <ci> CompoundExpression </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </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> <ci> &#8230; </ci> <apply> <apply> <power /> <ci> &#8472; </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> CompoundExpression </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </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> </list> <list> <cn type='integer'> 1 </cn> <apply> <ci> WeierstrassP </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </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> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <ci> &#8472; </ci> </apply> <apply> <ci> CompoundExpression </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </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> <ci> &#8230; </ci> <apply> <apply> <power /> <ci> &#8472; </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> CompoundExpression </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </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> </list> <list> <ci> &#8942; </ci> <ci> &#8942; </ci> <ci> &#8942; </ci> <ci> &#8945; </ci> <ci> &#8942; </ci> </list> <list> <cn type='integer'> 1 </cn> <apply> <ci> WeierstrassP </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <ci> n </ci> </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> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <ci> &#8472; </ci> </apply> <apply> <ci> CompoundExpression </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <ci> n </ci> </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> <ci> &#8230; </ci> <apply> <apply> <power /> <ci> &#8472; </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> CompoundExpression </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <ci> n </ci> </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> </list> </list> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <ci> WeierstrassSigma </ci> <apply> <sum /> <bvar> <ci> i </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <ci> Subscript </ci> <ci> z </ci> <ci> i </ci> </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> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <factorial /> <ci> k </ci> </apply> <apply> <power /> <apply> <power /> <apply> <ci> WeierstrassSigma </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <ci> k </ci> </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> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <product /> <bvar> <ci> j </ci> </bvar> <lowlimit> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <product /> <bvar> <ci> i </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <ci> WeierstrassSigma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <ci> i </ci> </apply> </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> </apply> </apply> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Det", "[", RowBox[List["Table", "[", RowBox[List[RowBox[List["If", "[", RowBox[List[RowBox[List["j", "\[Equal]", "0"]], ",", "1", ",", RowBox[List[SuperscriptBox["WeierstrassP", TagBox[RowBox[List["(", RowBox[List[RowBox[List["j", "-", "1"]], ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List[SubscriptBox["z_", "i_"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "]"]], ",", RowBox[List["{", RowBox[List["i_", ",", "0", ",", "n_"]], "}"]], ",", RowBox[List["{", RowBox[List["j", ",", "0", ",", "n_"]], "}"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], SubscriptBox["zz", "i"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], " ", RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List["k", "!"]], SuperscriptBox[RowBox[List["WeierstrassSigma", "[", RowBox[List[SubscriptBox["z", "k"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], RowBox[List["n", "+", "1"]]]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["i", "=", "1"]], RowBox[List["n", "-", "1"]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", RowBox[List["i", "+", "1"]]]], "n"], RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List[SubscriptBox["z", "j"], "-", SubscriptBox["zz", "i"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]










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





2001-10-29





© 1998-2014 Wolfram Research, Inc.