|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/03.17.13.0004.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Wronskian[KelvinBer[\[Nu], g[z]], KelvinBei[\[Nu], g[z]],
KelvinKer[\[Nu], g[z]], KelvinKei[\[Nu], g[z]], z] ==
-(Derivative[1][g][z]^6/g[z]^2)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]", ",", RowBox[List["g", "[", "z", "]"]]]], "]"]], ",", RowBox[List["KelvinBei", "[", RowBox[List["\[Nu]", ",", RowBox[List["g", "[", "z", "]"]]]], "]"]], ",", RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", RowBox[List["g", "[", "z", "]"]]]], "]"]], ",", RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]", ",", RowBox[List["g", "[", "z", "]"]]]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "6"], SuperscriptBox[RowBox[List["g", "[", "z", "]"]], "2"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<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> <msub> <mi> ber </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <mi> g </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <msub> <mi> bei </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <mi> g </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <msub> <mi> ker </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <mi> g </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <msub> <mi> kei </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <mi> g </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mtext> </mtext> <msup> <mrow> <msup> <mi> g </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> </mrow> <msup> <mrow> <mi> g </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> z </ci> </apply> <apply> <ci> KelvinBer </ci> <ci> ν </ci> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <apply> <ci> KelvinBei </ci> <ci> ν </ci> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <apply> <ci> KelvinKer </ci> <ci> ν </ci> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <apply> <ci> KelvinKei </ci> <ci> ν </ci> <apply> <times /> <ci> g </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <ci> g </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Wronskian", "[", RowBox[List[RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]_", ",", RowBox[List["g", "[", "z_", "]"]]]], "]"]], ",", RowBox[List["KelvinBei", "[", RowBox[List["\[Nu]_", ",", RowBox[List["g", "[", "z_", "]"]]]], "]"]], ",", RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]_", ",", RowBox[List["g", "[", "z_", "]"]]]], "]"]], ",", RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]_", ",", RowBox[List["g", "[", "z_", "]"]]]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "6"], SuperscriptBox[RowBox[List["g", "[", "z", "]"]], "2"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|