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variants of this functions
WeierstrassSigma




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassSigma[z,{g2,g3}] > Differentiation > Low-order differentiation > With respect to omega1





http://functions.wolfram.com/09.15.20.0013.02









  


  








Input Form





D[WeierstrassSigma[z, {Subscript[g, 2], Subscript[g, 3]}], Subscript[\[Omega], 1]] == (Subscript[\[Omega], 1]/(Pi Subscript[\[Omega], 3])) Sqrt[-(Subscript[\[Omega], 3]^2/Subscript[\[Omega], 1]^2)] (Subscript[\[Omega], 3] (WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] - WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]^2 - (1/12) Subscript[g, 2] z^2) + 2 Subscript[\[Eta], 3] (z WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] - 1)) WeierstrassSigma[z, {Subscript[g, 2], Subscript[g, 3]}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", SubscriptBox["\[Omega]", "1"]], RowBox[List["WeierstrassSigma", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[SubscriptBox["\[Omega]", "1"], RowBox[List["\[Pi]", " ", SubscriptBox["\[Omega]", "3"]]]], " ", SqrtBox[RowBox[List["-", FractionBox[SubsuperscriptBox["\[Omega]", "3", "2"], SubsuperscriptBox["\[Omega]", "1", "2"]]]]], RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["\[Omega]", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "-", SuperscriptBox[RowBox[List["WeierstrassZeta", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "2"], "-", RowBox[List[FractionBox["1", "12"], SubscriptBox["g", "2"], SuperscriptBox["z", "2"]]]]], ")"]]]], "+", RowBox[List["2", SubscriptBox["\[Eta]", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["z", " ", RowBox[List["WeierstrassZeta", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "-", "1"]], ")"]]]]]], ")"]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]]]]]]








MathML Form







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</mo> <mrow> <mfrac> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> </mfrac> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <msubsup> <mi> &#969; </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> <msubsup> <mi> &#969; </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#8472; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <msup> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[TagBox[&quot;z&quot;, Rule[Editable, True]], &quot;;&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], Rule[Editable, True]]]], &quot;,&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> <mo> &#8290; 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</ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <times /> <pi /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <ci> WeierstrassP </ci> <ci> z </ci> <list> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <ci> WeierstrassZeta </ci> <ci> z </ci> <list> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 12 </cn> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> &#951; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["\[Omega]_", "1"]]]], RowBox[List["WeierstrassSigma", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SubscriptBox["\[Omega]\[Omega]", "1"], " ", SqrtBox[RowBox[List["-", FractionBox[SubsuperscriptBox["\[Omega]\[Omega]", "3", "2"], SubsuperscriptBox["\[Omega]\[Omega]", "1", "2"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["\[Omega]\[Omega]", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "-", SuperscriptBox[RowBox[List["WeierstrassZeta", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "2"], "-", FractionBox[RowBox[List[SubscriptBox["gg", "2"], " ", SuperscriptBox["z", "2"]]], "12"]]], ")"]]]], "+", RowBox[List["2", " ", SubscriptBox["\[Eta]", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["z", " ", RowBox[List["WeierstrassZeta", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], "-", "1"]], ")"]]]]]], ")"]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], RowBox[List["\[Pi]", " ", SubscriptBox["\[Omega]\[Omega]", "3"]]]]]]]]


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





2002-12-18