|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/03.04.17.0009.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
BesselK[\[Nu], z] == (-(1/z^5))
(2 (3 + \[Nu]) (3 z^4 + 16 z^2 (2 + \[Nu]) (4 + \[Nu]) +
16 (1 + \[Nu]) (2 + \[Nu]) (4 + \[Nu]) (5 + \[Nu]))
BesselK[5 + \[Nu], z] - z (z^4 + 12 z^2 (2 + \[Nu]) (3 + \[Nu]) +
16 (1 + \[Nu]) (2 + \[Nu]) (3 + \[Nu]) (4 + \[Nu]))
BesselK[6 + \[Nu], z])
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["BesselK", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "5"]]]], RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["3", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["16", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "\[Nu]"]], ")"]]]], "+", RowBox[List["16", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["5", "+", "\[Nu]"]], ")"]]]]]], ")"]], " ", RowBox[List["BesselK", "[", RowBox[List[RowBox[List["5", "+", "\[Nu]"]], ",", "z"]], "]"]]]], "-", RowBox[List["z", " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", "4"], "+", RowBox[List["12", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["3", "+", "\[Nu]"]], ")"]]]], "+", RowBox[List["16", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["3", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "\[Nu]"]], ")"]]]]]], ")"]], " ", RowBox[List["BesselK", "[", RowBox[List[RowBox[List["6", "+", "\[Nu]"]], ",", "z"]], "]"]]]]]], ")"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> K </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mfrac> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <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> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 16 </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> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </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> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> K </mi> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 5 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> + </mo> <mrow> <mn> 12 </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> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </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> <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> 4 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> K </mi> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 6 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> BesselK </ci> <ci> ν </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <ci> BesselK </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 5 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <ci> BesselK </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 6 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BesselK", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["3", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["16", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "\[Nu]"]], ")"]]]], "+", RowBox[List["16", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["5", "+", "\[Nu]"]], ")"]]]]]], ")"]], " ", RowBox[List["BesselK", "[", RowBox[List[RowBox[List["5", "+", "\[Nu]"]], ",", "z"]], "]"]]]], "-", RowBox[List["z", " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", "4"], "+", RowBox[List["12", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["3", "+", "\[Nu]"]], ")"]]]], "+", RowBox[List["16", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["3", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "\[Nu]"]], ")"]]]]]], ")"]], " ", RowBox[List["BesselK", "[", RowBox[List[RowBox[List["6", "+", "\[Nu]"]], ",", "z"]], "]"]]]]]], SuperscriptBox["z", "5"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
){kind=small}
