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WeierstrassP




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassP[z,{g2,g3}] > Transformations > Related transformations > Other constructions





http://functions.wolfram.com/09.13.16.0027.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["z", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "-", 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"]]], "}"]]]], "]"]]]], ")"]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["z", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", RowBox[List["(", 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[SubscriptBox["z", "1"], ",", 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"]]], "}"]]]], "]"]]]], ")"]]]], "+", " ", RowBox[List[SubscriptBox["\[PartialD]", SubscriptBox["z", "1"]], RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["z", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", RowBox[List["3", " "]]]]], "}"]]]], "]"]]]]]], ")"]]]]]]]]








MathML Form







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Rule Form





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


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





2001-10-29