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Exp




Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Representations through more general functions > Through Meijer G > Classical cases for the direct function itself





http://functions.wolfram.com/01.03.26.0117.01









  


  








Input Form





E^z^(1/4) == 4 Sqrt[2] Pi^(5/2) MeijerG[{{}, {1/8, 3/8, 5/8, 7/8}}, {{0, 1/4, 1/2, 3/4}, {1/8, 3/8, 5/8, 7/8}}, z/256]








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]], "\[Equal]", RowBox[List["4", " ", SqrtBox["2"], " ", SuperscriptBox["\[Pi]", RowBox[List["5", "/", "2"]]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "8"], ",", FractionBox["3", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "4"], ",", FractionBox["1", "2"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "8"], ",", FractionBox["3", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"]]], "}"]]]], "}"]], ",", FractionBox["z", "256"]]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msup> <mi> &#8519; </mi> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </msup> <mo> &#63449; </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 8 </mn> </mrow> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mi> z </mi> <mn> 256 </mn> </mfrac> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 8 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 5 </mn> <mn> 8 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 7 </mn> <mn> 8 </mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 8 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 5 </mn> <mn> 8 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 7 </mn> <mn> 8 </mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;4&quot;, &quot;,&quot;, &quot;8&quot;]], RowBox[List[&quot;4&quot;, &quot;,&quot;, &quot;0&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[FractionBox[&quot;z&quot;, &quot;256&quot;], MeijerG, Rule[Editable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[FractionBox[&quot;1&quot;, &quot;8&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;3&quot;, &quot;8&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;5&quot;, &quot;8&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;7&quot;, &quot;8&quot;], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;1&quot;, &quot;4&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;1&quot;, &quot;2&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;3&quot;, &quot;4&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;1&quot;, &quot;8&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;3&quot;, &quot;8&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;5&quot;, &quot;8&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;7&quot;, &quot;8&quot;], MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <exponentiale /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <pi /> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <apply> <ci> MeijerG </ci> <list> <list /> <list> <cn type='rational'> 1 <sep /> 8 </cn> <cn type='rational'> 3 <sep /> 8 </cn> <cn type='rational'> 5 <sep /> 8 </cn> <cn type='rational'> 7 <sep /> 8 </cn> </list> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 4 </cn> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </list> <list> <cn type='rational'> 1 <sep /> 8 </cn> <cn type='rational'> 3 <sep /> 8 </cn> <cn type='rational'> 5 <sep /> 8 </cn> <cn type='rational'> 7 <sep /> 8 </cn> </list> </list> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 256 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", SuperscriptBox["z_", RowBox[List["1", "/", "4"]]]], "]"]], "\[RuleDelayed]", RowBox[List["4", " ", SqrtBox["2"], " ", SuperscriptBox["\[Pi]", RowBox[List["5", "/", "2"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "8"], ",", FractionBox["3", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "4"], ",", FractionBox["1", "2"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "8"], ",", FractionBox["3", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"]]], "}"]]]], "}"]], ",", FractionBox["z", "256"]]], "]"]]]]]]]]


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





2007-05-02