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WeierstrassZeta






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassZeta[z,{g2,g3}] > Transformations > Related transformations > General fractions of half-periods





http://functions.wolfram.com/09.17.16.0013.01









  


  










Input Form





WeierstrassZeta[z, WeierstrassInvariants[{Subscript[\[Omega], 1]/n, Subscript[\[Omega], 3]}]] == WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] + Sum[WeierstrassZeta[z + (2 k Subscript[\[Omega], 1])/n, {Subscript[g, 2], Subscript[g, 3]}] + z WeierstrassP[(2 k Subscript[\[Omega], 1])/n, {Subscript[g, 2], Subscript[g, 3]}] - (2 k Subscript[\[Eta], 1])/n, {k, 1, n - 1}] /; Element[n, Integers] && n > 0










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassZeta", "[", RowBox[List["z_", ",", RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List[FractionBox[SubscriptBox["\[Omega]_", "1"], "n_"], ",", SubscriptBox["\[Omega]_", "3"]]], "}"]], "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], RowBox[List["n", "-", "1"]]], RowBox[List["(", RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["z", "+", FractionBox[RowBox[List["2", " ", "k", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]], "n"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "+", RowBox[List["z", " ", RowBox[List["WeierstrassP", "[", RowBox[List[FractionBox[RowBox[List["2", " ", "k", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]], "n"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "-", FractionBox[RowBox[List["2", " ", "k", " ", SubscriptBox["\[Eta]", "1"]]], "n"]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]










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





2001-10-29





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