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ArcSin




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSin[z] > Series representations > Generalized power series > Expansions at z==0 > For small integer powers of the function > For the second power





http://functions.wolfram.com/01.12.06.0040.01









  


  








Input Form





ArcSin[z]^2 \[Proportional] z^2 + z^4/3 + (8 z^6)/45 + O[z^8]








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox[RowBox[List["ArcSin", "[", "z", "]"]], "2"], "\[Proportional]", RowBox[List[SuperscriptBox["z", "2"], "+", FractionBox[SuperscriptBox["z", "4"], "3"], "+", FractionBox[RowBox[List["8", " ", SuperscriptBox["z", "6"]]], "45"], "+", RowBox[List["O", "[", SuperscriptBox["z", "8"], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msup> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8733; </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mn> 3 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mn> 45 </mn> </mfrac> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <power /> <apply> <arcsin /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <cn type='integer'> 45 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["ArcSin", "[", "z_", "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["z", "2"], "+", FractionBox[SuperscriptBox["z", "4"], "3"], "+", FractionBox[RowBox[List["8", " ", SuperscriptBox["z", "6"]]], "45"], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "8"]]]]]]]


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





2007-05-02