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http://functions.wolfram.com/09.13.27.0006.01
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WeierstrassP[Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}] -
WeierstrassP[Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}] ==
-((WeierstrassSigma[Subscript[z, 1] + Subscript[z, 2],
{Subscript[g, 2], Subscript[g, 3]}] WeierstrassSigma[
Subscript[z, 1] - Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}])/
(WeierstrassSigma[Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}]^2
WeierstrassSigma[Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}]^2))
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["z", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "-", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["z", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "\[Equal]", RowBox[List["-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List[SubscriptBox["z", "1"], "+", SubscriptBox["z", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List[SubscriptBox["z", "1"], "-", SubscriptBox["z", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["WeierstrassSigma", "[", RowBox[List[SubscriptBox["z", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["WeierstrassSigma", "[", RowBox[List[SubscriptBox["z", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "2"]]], ")"]]]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> ℘ </mi> <mo> ⁡ </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> <mo> - </mo> <mrow> <mi> ℘ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 2 </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> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <semantics> <mrow> <mi> σ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> z </mi> <mn> 2 </mn> </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["\[Sigma]", "(", RowBox[List[RowBox[List[TagBox[RowBox[List[SubscriptBox["z", "1"], "+", SubscriptBox["z", "2"]]], Rule[Editable, True]], ";", TagBox[SubscriptBox["g", "2"], Rule[Editable, True]]]], ",", TagBox[SubscriptBox["g", "3"], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <mrow> <mi> σ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 2 </mn> </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["\[Sigma]", "(", RowBox[List[RowBox[List[TagBox[RowBox[List[SubscriptBox["z", "1"], "-", SubscriptBox["z", "2"]]], Rule[Editable, True]], ";", TagBox[SubscriptBox["g", "2"], Rule[Editable, True]]]], ",", TagBox[SubscriptBox["g", "3"], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> </mrow> <mrow> <msup> <semantics> <mrow> <mi> σ </mi> <mo> ⁡ </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> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Sigma]", "(", RowBox[List[RowBox[List[TagBox[SubscriptBox["z", "1"], Rule[Editable, True]], ";", TagBox[SubscriptBox["g", "2"], Rule[Editable, True]]]], ",", TagBox[SubscriptBox["g", "3"], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <semantics> <mrow> <mi> σ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 2 </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> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Sigma]", "(", RowBox[List[RowBox[List[TagBox[SubscriptBox["z", "2"], Rule[Editable, True]], ";", TagBox[SubscriptBox["g", "2"], Rule[Editable, True]]]], ",", TagBox[SubscriptBox["g", "3"], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <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> <times /> <cn type='integer'> -1 </cn> <apply> <ci> WeierstrassP </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </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> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> WeierstrassSigma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </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> <ci> WeierstrassSigma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </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> <power /> <apply> <times /> <apply> <power /> <apply> <ci> WeierstrassSigma </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> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> WeierstrassSigma </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </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> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["z_", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "-", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["z_", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List[SubscriptBox["zz", "1"], "+", SubscriptBox["zz", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List[SubscriptBox["zz", "1"], "-", SubscriptBox["zz", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["WeierstrassSigma", "[", RowBox[List[SubscriptBox["zz", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["WeierstrassSigma", "[", RowBox[List[SubscriptBox["zz", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "2"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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