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Sin




Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Representations through more general functions > Through other functions > Involving some elliptic-type functions





http://functions.wolfram.com/01.06.26.0090.01









  


  








Input Form





Sin[z] == (Sqrt[3/2] WeierstrassSigma[Sqrt[2/3] z, {3, 1}])/E^(z^2/6)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Sin", "[", "z", "]"]], "\[Equal]", RowBox[List[SqrtBox[FractionBox["3", "2"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "6"]]]], RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List[SqrtBox[FractionBox["2", "3"]], " ", "z"]], ",", RowBox[List["{", RowBox[List["3", ",", "1"]], "}"]]]], "]"]], " "]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mtext> </mtext> <mrow> <msqrt> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </msqrt> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mn> 6 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#963; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <msqrt> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </msqrt> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ; </mo> <mn> 3 </mn> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Sigma]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[TagBox[RowBox[List[SqrtBox[FractionBox[&quot;2&quot;, &quot;3&quot;]], &quot; &quot;, &quot;z&quot;]], Rule[Editable, True]], &quot;;&quot;, TagBox[&quot;3&quot;, Rule[Editable, True]]]], &quot;,&quot;, TagBox[&quot;1&quot;, Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sin /> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 6 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> WeierstrassSigma </ci> <apply> <times /> <apply> <power /> <cn type='rational'> 2 <sep /> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <list> <cn type='integer'> 3 </cn> <cn type='integer'> 1 </cn> </list> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sin", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox[FractionBox["3", "2"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "6"]]]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List[SqrtBox[FractionBox["2", "3"]], " ", "z"]], ",", RowBox[List["{", RowBox[List["3", ",", "1"]], "}"]]]], "]"]]]]]]]]


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





2001-10-29