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WeierstrassP






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassP[z,{g2,g3}] > Transformations > Addition formulas > Translation by half-periods





http://functions.wolfram.com/09.13.16.0007.01









  


  










Input Form





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]]










Standard Form





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MathML Form







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</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> &#8472; </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>










Rule Form





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"]]], "}"]]]], "]"]]]]]]]]]]]]]]]










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





2001-10-29





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