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Sqrt




Mathematica Notation

Traditional Notation









Elementary Functions > Sqrt[z] > Continued fraction representations





http://functions.wolfram.com/01.01.10.0006.01









  


  








Input Form





Sqrt[1 + z] == 1 + 4 ContinueFraction[{z/16, 1/2}, {k, 1, Infinity}]








Standard Form





Cell[BoxData[RowBox[List[SqrtBox[RowBox[List["1", "+", "z"]]], "\[Equal]", RowBox[List["1", "+", RowBox[List["4", RowBox[List["ContinueFraction", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["z", "16"], ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["k", ",", "1", ",", "\[Infinity]"]], "}"]]]], "]"]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> z </mi> </mrow> </msqrt> <mo> &#63449; </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msubsup> <mrow> <msub> <mi> &#922; </mi> <mi> k </mi> </msub> <mo> ( </mo> <mrow> <mfrac> <mi> z </mi> <mn> 16 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mn> 1 </mn> <mi> &#8734; </mi> </msubsup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <apply> <ci> Subscript </ci> <ci> &#922; </ci> <ci> k </ci> </apply> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 16 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <infinity /> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SqrtBox[RowBox[List["1", "+", "z_"]]], "]"]], "\[RuleDelayed]", RowBox[List["1", "+", RowBox[List["4", " ", RowBox[List["ContinueFraction", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["z", "16"], ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["k", ",", "1", ",", "\[Infinity]"]], "}"]]]], "]"]]]]]]]]]]










Contributed by





Andreas Lauschke (2006)


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





2007-05-02