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http://functions.wolfram.com/01.07.26.0089.01
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Cos[z^(1/3)]/E^(z^(1/3)/Sqrt[3]) ==
(1/2) Sqrt[3] MeijerG[{{}, {1/2}}, {{0, 1/3, 2/3}, {1/2}},
(8 z)/(81 Sqrt[3])]
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Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "3"]]], SqrtBox["3"]]]]], " ", RowBox[List["Cos", "[", SuperscriptBox["z", RowBox[List["1", "/", "3"]]], "]"]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", SqrtBox["3"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "3"], ",", FractionBox["2", "3"]]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]]]], "}"]], ",", FractionBox[RowBox[List["8", " ", "z"]], RowBox[List["81", " ", SqrtBox["3"]]]]]], "]"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <mfrac> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <msqrt> <mn> 3 </mn> </msqrt> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mroot> <mi> z </mi> <mn> 3 </mn> </mroot> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <msqrt> <mn> 3 </mn> </msqrt> <mo> ⁢ </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mrow> <mn> 81 </mn> <mo> ⁢ </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> </mfrac> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["1", ",", "4"]], RowBox[List["3", ",", "0"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[FractionBox[RowBox[List["8", " ", "z"]], RowBox[List["81", " ", SqrtBox["3"]]]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["2", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <power /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <cos /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> MeijerG </ci> <list> <list /> <list> <cn type='rational'> 1 <sep /> 2 </cn> </list> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 3 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </list> <list> <cn type='rational'> 1 <sep /> 2 </cn> </list> </list> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 81 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["z_", RowBox[List["1", "/", "3"]]], SqrtBox["3"]]]]], " ", RowBox[List["Cos", "[", SuperscriptBox["z_", RowBox[List["1", "/", "3"]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", SqrtBox["3"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "3"], ",", FractionBox["2", "3"]]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]]]], "}"]], ",", FractionBox[RowBox[List["8", " ", "z"]], RowBox[List["81", " ", SqrtBox["3"]]]]]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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