Weierstrass zeta function values at half periods: Primary definition (formula 09.21.02.0001)

WeierstrassZetaHalfPeriodValues

$Mathematica Notation$

Elliptic Functions

WeierstrassZetaHalfPeriodValues[{g₂,g₃}]

Primary definition

http://functions.wolfram.com/09.21.02.0001.01

Input Form

{Subscript[\[Eta], 1], Subscript[\[Eta], 2], Subscript[\[Eta], 3]} == WeierstrassZetaHalfPeriodValues[{Subscript[g, 2], Subscript[g, 3]}] /; {Subscript[\[Eta], 1], Subscript[\[Eta], 2], Subscript[\[Eta], 3]} == {WeierstrassZeta[Subscript[\[Omega], 1], {Subscript[g, 2], Subscript[g, 3]}], WeierstrassZeta[Subscript[\[Omega], 2], {Subscript[g, 2], Subscript[g, 3]}], WeierstrassZeta[ Subscript[\[Omega], 3], {Subscript[g, 2], Subscript[g, 3]}]} && {Subscript[\[Omega], 1], Subscript[\[Omega], 3]} == WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}] && Subscript[\[Omega], 2] == -Subscript[\[Omega], 1] - Subscript[\[Omega], 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[SubscriptBox["\[Eta]_", "1"], ",", SubscriptBox["\[Eta]_", "2"], ",", SubscriptBox["\[Eta]_", "3"]]], "}"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["WeierstrassZetaHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["\[Eta]", "1"], ",", SubscriptBox["\[Eta]", "2"], ",", SubscriptBox["\[Eta]", "3"]]], "}"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], ",", RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], ",", RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]", "3"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "}"]]]], "&&", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "\[Equal]", RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]]]], "&&", RowBox[List[SubscriptBox["\[Omega]", "2"], "\[Equal]", RowBox[List[RowBox[List["-", SubscriptBox["\[Omega]", "1"]]], "-", SubscriptBox["\[Omega]", "3"]]]]]]]]]]]]]

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

2001-10-29