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http://functions.wolfram.com/03.02.26.0131.01
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BesselI[-2 - \[Nu], z] BesselI[\[Nu], z] ==
(-Sqrt[2 Pi]) MeijerG[{{0, 1/2}, {1/4}},
{{1}, {1 + \[Nu], -1, -1 - \[Nu], 1/4}}, z, 1/2] +
(4 (1 + \[Nu]) Sin[Pi \[Nu]])/(Pi z^2)
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BesselI", "[", RowBox[List[RowBox[List[RowBox[List["-", "2"]], "-", "\[Nu]"]], ",", "z"]], "]"]], " ", RowBox[List["BesselI", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", FractionBox["1", "4"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", RowBox[List["-", "1"]], ",", RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]"]], ",", FractionBox["1", "4"]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]], "+", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], RowBox[List["\[Pi]", " ", SuperscriptBox["z", "2"]]]]]]]]]]
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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> <mrow> <msub> <mi> I </mi> <mrow> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo>  </mo> <mrow> <mfrac> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> - </mo> <mrow> <msqrt> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </msqrt> <mo> ⁢ </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 5 </mn> </mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 1 </mn> <mo> , </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["3", ",", "5"]], RowBox[List["1", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox["z", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]], MeijerG], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox["1", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["\[Nu]", "+", "1"]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", "1"]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "1"]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <ci> BesselI </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <cn type='integer'> -2 </cn> </apply> <ci> z </ci> </apply> <apply> <ci> BesselI </ci> <ci> ν </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <apply> <sin /> <apply> <times /> <pi /> <ci> ν </ci> </apply> </apply> <apply> <power /> <apply> <times /> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> MeijerG </ci> <list> <list> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </list> <list> <cn type='rational'> 1 <sep /> 4 </cn> </list> </list> <list> <list> <cn type='integer'> 1 </cn> </list> <list> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </list> </list> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["BesselI", "[", RowBox[List[RowBox[List[RowBox[List["-", "2"]], "-", "\[Nu]_"]], ",", "z_"]], "]"]], " ", RowBox[List["BesselI", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", FractionBox["1", "4"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", RowBox[List["-", "1"]], ",", RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]"]], ",", FractionBox["1", "4"]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]], "+", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], RowBox[List["\[Pi]", " ", SuperscriptBox["z", "2"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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