
|

|

|

|

|
|

|

|

|

|

|
|

|

|

|

|

|
|

|

|

|

|
|

|

|

|

|
|

|

|

|

|

|
http://functions.wolfram.com/03.04.13.0026.01
|
|

|

|

|

|
|
|
|

|

|

|

|
|

|

|

|

|

|
Wronskian[s^z BesselI[\[Nu], a r^z], s^z BesselK[\[Nu], a r^z], z] ==
(-s^(2 z)) Log[r]
|
|

|

|

|

|
|

|

|

|

|
|

|

|

|

|

|
Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SuperscriptBox["s", "z"], " ", RowBox[List["BesselI", "[", RowBox[List["\[Nu]", ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]]]], ",", RowBox[List[SuperscriptBox["s", "z"], " ", RowBox[List["BesselK", "[", RowBox[List["\[Nu]", ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", SuperscriptBox["s", RowBox[List["2", " ", "z"]]]]], " ", RowBox[List["Log", "[", "r", "]"]]]]]]]]
|
|

|

|

|

|
|

|

|

|

|
|

|

|

|

|

|
|

|

|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> W </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mrow> <msup> <mi> s </mi> <mi> z </mi> </msup> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msup> <mi> s </mi> <mi> z </mi> </msup> <mo> ⁢ </mo> <mrow> <msub> <mi> K </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <msup> <mi> s </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <ci> s </ci> <ci> z </ci> </apply> <apply> <ci> BesselI </ci> <ci> ν </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> s </ci> <ci> z </ci> </apply> <apply> <ci> BesselK </ci> <ci> ν </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <ln /> <ci> r </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|

|

|

|

|

| 
| 
| 
| 
| | 
| 
| 
| 
| 
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SuperscriptBox["s_", "z_"], " ", RowBox[List["BesselI", "[", RowBox[List["\[Nu]_", ",", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"]]]]], "]"]]]], ",", RowBox[List[SuperscriptBox["s_", "z_"], " ", RowBox[List["BesselK", "[", RowBox[List["\[Nu]_", ",", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"]]]]], "]"]]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", SuperscriptBox["s", RowBox[List["2", " ", "z"]]]]], " ", RowBox[List["Log", "[", "r", "]"]]]]]]]] |
| 
| 
| 
| 
|
|

|

|

|

|
Date Added to functions.wolfram.com (modification date)
|
|

|

|

|

|

|
|

|

|

|

|
|
 |
|
|