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variants of this functions
EulerE




Mathematica Notation

Traditional Notation









Polynomials > EulerE[n,z] > Inequalities





http://functions.wolfram.com/05.13.29.0001.01









  


  








Input Form





0 < EulerE[2 n, x] < Abs[EulerE[2 n]]/4^n /; Element[n, Integers] && n > 0 && 0 < x < 1/2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["0", "<", RowBox[List["EulerE", "[", RowBox[List[RowBox[List["2", " ", "n"]], ",", "x"]], "]"]], "<", RowBox[List[SuperscriptBox["4", RowBox[List["-", "n"]]], " ", RowBox[List["Abs", "[", RowBox[List["EulerE", "[", RowBox[List["2", " ", "n"]], "]"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]], "\[And]", RowBox[List["0", "<", "x", "<", FractionBox["1", "2"]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mn> 0 </mn> <mo> &lt; </mo> <mrow> <msub> <semantics> <mi> E </mi> <annotation encoding='Mathematica'> TagBox[&quot;E&quot;, EulerE] </annotation> </semantics> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> n </mi> </mrow> </msub> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &lt; </mo> <mrow> <msup> <mn> 4 </mn> <mrow> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <msub> <semantics> <mi> E </mi> <annotation encoding='Mathematica'> TagBox[&quot;E&quot;, EulerE] </annotation> </semantics> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> n </mi> </mrow> </msub> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mn> 0 </mn> <mo> &lt; </mo> <mi> x </mi> <mo> &lt; </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <lt /> <cn type='integer'> 0 </cn> <apply> <ci> EulerE </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <ci> x </ci> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 4 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> <apply> <abs /> <apply> <ci> EulerE </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <integers /> </apply> </apply> <apply> <lt /> <cn type='integer'> 0 </cn> <ci> x </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["0", "<", RowBox[List["EulerE", "[", RowBox[List[RowBox[List["2", " ", "n"]], ",", "x"]], "]"]], "<", RowBox[List[SuperscriptBox["4", RowBox[List["-", "n"]]], " ", RowBox[List["Abs", "[", RowBox[List["EulerE", "[", RowBox[List["2", " ", "n"]], "]"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]], "&&", RowBox[List["0", "<", "x", "<", FractionBox["1", "2"]]]]]]]]]


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





2001-10-29