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WeierstrassZetaHalfPeriodValues






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassZetaHalfPeriodValues[{g2,g3}] > Representations through equivalent functions > With related functions > Involving theta functions





http://functions.wolfram.com/09.21.27.0003.01









  


  










Input Form





Subscript[\[Eta], 1]^2 == (Subscript[g, 2]/6 - Subscript[e, i]^2) Subscript[\[Omega], 1]^2 - ((Pi^2 Subscript[\[Eta], 1])/ (2 Subscript[\[Omega], 1])) (Derivative[0, 2, 0][EllipticTheta][i + 1, 0, q]/EllipticTheta[i + 1, 0, q]) - (Pi^4/(48 Subscript[\[Omega], 1]^2)) (Derivative[0, 4, 0][EllipticTheta][i + 1, 0, q]/ EllipticTheta[i + 1, 0, q]) /; Element[i, {1, 2, 3}]










Standard Form





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MathML Form







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</ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 2 </cn> </list> <apply> <ci> Subscript </ci> <ci> &#977; </ci> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> 0 </cn> <ci> q </ci> </apply> <apply> <power /> <apply> <ci> EllipticTheta </ci> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 48 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#977; </ci> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> 0 </cn> <ci> q </ci> </apply> <apply> <power /> <apply> <ci> EllipticTheta </ci> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> i </ci> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 2 </cn> <cn type='integer'> 3 </cn> </list> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SubsuperscriptBox["\[Eta]_", "1", "2"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[FractionBox[SubscriptBox["g", "2"], "6"], "-", SubsuperscriptBox["e", "i", "2"]]], ")"]], " ", SubsuperscriptBox["\[Omega]", "1", "2"]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", SubscriptBox["\[Eta]\[Eta]", "1"]]], ")"]], " ", RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "2", ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]], ")"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "4"], " ", RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "4", ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["48", " ", SubsuperscriptBox["\[Omega]", "1", "2"]]], ")"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]]]]]]], "/;", RowBox[List["i", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]]]]]]]]










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





2001-10-29





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