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http://functions.wolfram.com/09.13.16.0007.01
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WeierstrassP[Subscript[z, 1] \[PlusMinus] Subscript[z, 2],
{Subscript[g, 2], Subscript[g, 3]}] ==
WeierstrassP[Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}] -
(1/2) D[(WeierstrassPPrime[Subscript[z, 1], {Subscript[g, 2],
Subscript[g, 3]}] \[PlusMinus] WeierstrassPPrime[Subscript[z, 2],
{Subscript[g, 2], Subscript[g, 3]}])/
(WeierstrassP[Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}] -
WeierstrassP[Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}]),
Subscript[z, 1]]
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Cell[BoxData[RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List[RowBox[List[SubscriptBox["z", "1"], "\[PlusMinus]", SubscriptBox["z", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["z", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "-", RowBox[List[FractionBox["1", "2"], RowBox[List[SubscriptBox["\[PartialD]", SubscriptBox["z", "1"]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["z", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "\[PlusMinus]", RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["z", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], ")"]], "/", 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"]]], "}"]]]], "]"]]]], ")"]]]]]]]]]]]]]]
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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> <mi> ℘ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ± </mo> <mi> a </mi> </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> <mo> ⩵ </mo> <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> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mfrac> <mo> ∂ </mo> <mrow> <mo> ∂ </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> ⁢ </mo> <mfrac> <mrow> <mrow> <msup> <mi> ℘ </mi> <mo> ′ </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> <mo> ± </mo> <mrow> <msup> <mi> ℘ </mi> <mo> ′ </mo> </msup> <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> <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> </mfrac> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ℘ </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> z </ms> <ms> 1 </ms> </apply> <ms> ± </ms> <ms> a </ms> </list> </apply> <ms> ; </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 2 </ms> </apply> </list> </apply> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 3 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <ms> ⩵ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ℘ </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> z </ms> <ms> 1 </ms> </apply> <ms> ; </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 2 </ms> </apply> </list> </apply> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 3 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <ms> - </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <ms> 2 </ms> </apply> <apply> <ci> FractionBox </ci> <apply> <ci> ErrorBox </ci> <ms> ∂ </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> ∂ </ms> <apply> <ci> SubscriptBox </ci> <ms> z </ms> <ms> 1 </ms> </apply> </list> </apply> </apply> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SuperscriptBox </ci> <ms> ℘ </ms> <ms> ′ </ms> </apply> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> z </ms> <ms> 1 </ms> </apply> <ms> ; </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 2 </ms> </apply> </list> </apply> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 3 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <ms> ± </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SuperscriptBox </ci> <ms> ℘ </ms> <ms> ′ </ms> </apply> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> z </ms> <ms> 2 </ms> </apply> <ms> ; </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 2 </ms> </apply> </list> </apply> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 3 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ℘ </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> z </ms> <ms> 1 </ms> </apply> <ms> ; </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 2 </ms> </apply> </list> </apply> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 3 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <ms> - </ms> <apply> <ci> RowBox </ci> <list> <ms> ℘ </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> z </ms> <ms> 2 </ms> </apply> <ms> ; </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 2 </ms> </apply> </list> </apply> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 3 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </apply> </list> </apply> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassP", "[", RowBox[List[RowBox[List[SubscriptBox["z_", "1"], "\[PlusMinus]", SubscriptBox["z_", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["zz", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "-", RowBox[List[FractionBox["1", "2"], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["zz", "1"]]]], FractionBox[RowBox[List[RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["zz", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "\[PlusMinus]", RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["zz", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["zz", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "-", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["zz", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]]]]]]]]]]]]] |
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