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http://functions.wolfram.com/03.16.26.0004.01
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KelvinKer[z]^2 == (1/(16 Sqrt[Pi])) MeijerG[{{}, {}}, {{0, 0, 0, 1/2}, {}},
z^4/64] + (1/8) Sqrt[Pi/2] MeijerG[{{}, {1/4, 3/4}},
{{0, 0, 0, 1/2, 1/2}, {1/2}}, z^4/16] /;
Inequality[-(Pi/4), Less, Arg[z], LessEqual, Pi/4]
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Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["KelvinKer", "[", "z", "]"]], "2"], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["16", " ", SqrtBox["\[Pi]"]]]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "0", ",", "0", ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "4"], "64"]]], "]"]]]], "+", RowBox[List[FractionBox["1", "8"], " ", SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["3", "4"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "0", ",", "0", ",", FractionBox["1", "2"], ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "4"], "16"]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "4"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "4"]]]]]]]
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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> <mrow> <mi> ker </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo>  </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> </mrow> </mfrac> <mo> ⁢ </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mn> 64 </mn> </mfrac> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> <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["0", ",", "4"]], RowBox[List["4", ",", "0"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[FractionBox[SuperscriptBox["z", "4"], "64"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <msqrt> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> </msqrt> <mo> ⁢ </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 6 </mn> </mrow> <mrow> <mn> 5 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mn> 16 </mn> </mfrac> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </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["2", ",", "6"]], RowBox[List["5", ",", "0"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[FractionBox[SuperscriptBox["z", "4"], "16"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[FractionBox["1", "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mi> π </mi> <mn> 4 </mn> </mfrac> </mrow> <mo> < </mo> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ≤ </mo> <mfrac> <mi> π </mi> <mn> 4 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <apply> <ci> KelvinKer </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> MeijerG </ci> <list> <list /> <list /> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </list> <list /> </list> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <cn type='integer'> 64 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <power /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> MeijerG </ci> <list> <list /> <list> <cn type='rational'> 1 <sep /> 4 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </list> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </list> <list> <cn type='rational'> 1 <sep /> 2 </cn> </list> </list> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <cn type='integer'> 16 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Inequality </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <lt /> <apply> <arg /> <ci> z </ci> </apply> <leq /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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