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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/09.13.16.0010.01









  


  










Input Form





WeierstrassP[Subscript[z, 1] + Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}] + WeierstrassP[Subscript[z, 1] - Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}] == 2 WeierstrassP[Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}] + (1/(WeierstrassP[Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}] - WeierstrassP[Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}])^2) (WeierstrassPPrime[Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}]^ 2 - D[WeierstrassPPrime[Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}], Subscript[z, 1]] (WeierstrassP[Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}] - WeierstrassP[Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}]))










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List[RowBox[List[SubscriptBox["z_", "1"], "+", SubscriptBox["z_", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "+", RowBox[List["WeierstrassP", "[", RowBox[List[RowBox[List[SubscriptBox["z_", "1"], "-", SubscriptBox["z_", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["2", " ", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["zz", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], "+", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["zz", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "2"], "-", RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["zz", "1"]]]], RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["zz", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], " ", RowBox[List["(", 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"]]], "}"]]]], "]"]]]], ")"]]]]]], SuperscriptBox[RowBox[List["(", 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"]]], "}"]]]], "]"]]]], ")"]], "2"]]]]]]]]










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





2001-10-29