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ArcSin




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSin[z] > Integral representations > On the real axis > Of the direct function





http://functions.wolfram.com/01.12.07.0001.01









  


  








Input Form





ArcSin[z] == z Integrate[1/Sqrt[1 - z^2 t^2], {t, 0, 1}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["ArcSin", "[", "z", "]"]], "\[Equal]", RowBox[List["z", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[FractionBox["1", SqrtBox[RowBox[List["1", "-", RowBox[List[SuperscriptBox["z", "2"], " ", SuperscriptBox["t", "2"]]]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mn> 1 </mn> </msubsup> <mrow> <mfrac> <mn> 1 </mn> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> t </mi> <mn> 2 </mn> </msup> </mrow> </mrow> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arcsin /> <ci> z </ci> </apply> <apply> <times /> <ci> z </ci> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <cn type='integer'> 1 </cn> </uplimit> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> t </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["z", " ", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[FractionBox["1", SqrtBox[RowBox[List["1", "-", RowBox[List[SuperscriptBox["z", "2"], " ", SuperscriptBox["t", "2"]]]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]]]


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





2001-10-29