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http://functions.wolfram.com/03.02.17.0012.01
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BesselI[\[Nu], z] == (1/z^3) (z (z^2 + 4 (-2 + \[Nu]) (-1 + \[Nu]))
BesselI[-4 + \[Nu], z] - 4 (z^2 + 2 (-3 + \[Nu]) (-1 + \[Nu]))
(-2 + \[Nu]) BesselI[-3 + \[Nu], z])
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Cell[BoxData[RowBox[List[RowBox[List["BesselI", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", SuperscriptBox["z", "3"]], RowBox[List["(", RowBox[List[RowBox[List["z", " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List[RowBox[List["-", "4"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]]]], ")"]]]]]]]]
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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> <msub> <mi> I </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 4 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 3 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> BesselI </ci> <ci> ν </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> BesselI </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -4 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -2 </cn> </apply> <apply> <ci> BesselI </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -3 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BesselI", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["z", " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ")"]]]]]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List[RowBox[List["-", "4"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]]]], SuperscriptBox["z", "3"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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