|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/01.07.13.0012.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Wronskian[z^s Cos[a z^r], z^s Sin[a z^r], z] == a r z^(-1 + r + 2 s)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SuperscriptBox["z", "s"], RowBox[List["Cos", "[", RowBox[List["a", " ", SuperscriptBox["z", "r"]]], "]"]]]], ",", RowBox[List[SuperscriptBox["z", "s"], RowBox[List["Sin", "[", RowBox[List["a", " ", SuperscriptBox["z", "r"]]], "]"]]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["a", " ", "r", " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "1"]], "+", "r", "+", RowBox[List["2", " ", "s"]]]]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<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> z </mi> <mi> s </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msup> <mi> z </mi> <mi> s </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> r </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mi> r </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </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> z </ci> <ci> s </ci> </apply> <apply> <cos /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> s </ci> </apply> <apply> <sin /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <ci> a </ci> <ci> r </ci> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> r </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </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[SuperscriptBox["z_", "s_"], " ", RowBox[List["Cos", "[", RowBox[List["a_", " ", SuperscriptBox["z_", "r_"]]], "]"]]]], ",", RowBox[List[SuperscriptBox["z_", "s_"], " ", RowBox[List["Sin", "[", RowBox[List["a_", " ", SuperscriptBox["z_", "r_"]]], "]"]]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["a", " ", "r", " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "1"]], "+", "r", "+", RowBox[List["2", " ", "s"]]]]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|