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E






Mathematica Notation

Traditional Notation









Constants > E > Series representations > Generalized power series > Expansions for e1/2





http://functions.wolfram.com/02.05.06.0026.01









  


  










Input Form





Sqrt[E] == Sum[(4 k + 3)/((2 k + 1)! 2^(2 k + 1)), {k, 0, Infinity}]










Standard Form





Cell[BoxData[RowBox[List[SqrtBox["\[ExponentialE]"], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["4", "k"]], "+", "3"]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", "k"]], "+", "1"]], ")"]], "!"]], SuperscriptBox["2", RowBox[List[RowBox[List["2", "k"]], "+", "1"]]]]]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msqrt> <mi> &#8519; </mi> </msqrt> <mo> &#63449; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mfrac> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <msup> <mn> 2 </mn> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <exponentiale /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> k </ci> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <factorial /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SqrtBox["\[ExponentialE]"], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["4", " ", "k"]], "+", "3"]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], "!"]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]]]]]]]]]]]










Contributed by





H. J. Brothers










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





2007-05-02