|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/11.02.13.0010.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Wronskian[s^z MathieuS[a, q, b r^z], s^z MathieuC[a, q, b r^z], z] ==
b r^z s^(2 z) Log[r] (MathieuCPrime[a, q, 0] MathieuS[a, q, 0] -
MathieuC[a, q, 0] MathieuSPrime[a, q, 0])
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SuperscriptBox["s", "z"], " ", RowBox[List["MathieuS", "[", RowBox[List["a", ",", "q", ",", RowBox[List["b", " ", SuperscriptBox["r", "z"]]]]], "]"]]]], ",", RowBox[List[SuperscriptBox["s", "z"], " ", RowBox[List["MathieuC", "[", RowBox[List["a", ",", "q", ",", RowBox[List["b", " ", SuperscriptBox["r", "z"]]]]], "]"]]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["b", " ", SuperscriptBox["r", "z"], " ", SuperscriptBox["s", RowBox[List["2", " ", "z"]]], " ", RowBox[List["Log", "[", "r", "]"]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["MathieuCPrime", "[", RowBox[List["a", ",", "q", ",", "0"]], "]"]], " ", RowBox[List["MathieuS", "[", RowBox[List["a", ",", "q", ",", "0"]], "]"]]]], "-", RowBox[List[RowBox[List["MathieuC", "[", RowBox[List["a", ",", "q", ",", "0"]], "]"]], " ", RowBox[List["MathieuSPrime", "[", RowBox[List["a", ",", "q", ",", "0"]], "]"]]]]]], ")"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<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> <mi> Ce </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msup> <mi> s </mi> <mi> z </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> Se </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> <mo> ⁢ </mo> <msup> <mi> s </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msup> <mi> Ce </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Se </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mi> Ce </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> Se </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> q </mi> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <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> Ce </ci> <ci> a </ci> <ci> q </ci> <apply> <times /> <ci> b </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> Se </ci> <ci> a </ci> <ci> q </ci> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> <apply> <power /> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <ln /> <ci> r </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <ci> Ce </ci> </apply> <ci> a </ci> <ci> q </ci> <cn type='integer'> 0 </cn> </apply> <apply> <ci> Se </ci> <ci> a </ci> <ci> q </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Ce </ci> <ci> a </ci> <ci> q </ci> <cn type='integer'> 0 </cn> </apply> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <ci> Se </ci> </apply> <ci> a </ci> <ci> q </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </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["MathieuS", "[", RowBox[List["a_", ",", "q_", ",", RowBox[List["b_", " ", SuperscriptBox["r_", "z_"]]]]], "]"]]]], ",", RowBox[List[SuperscriptBox["s_", "z_"], " ", RowBox[List["MathieuC", "[", RowBox[List["a_", ",", "q_", ",", RowBox[List["b_", " ", SuperscriptBox["r_", "z_"]]]]], "]"]]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["b", " ", SuperscriptBox["r", "z"], " ", SuperscriptBox["s", RowBox[List["2", " ", "z"]]], " ", RowBox[List["Log", "[", "r", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["MathieuCPrime", "[", RowBox[List["a", ",", "q", ",", "0"]], "]"]], " ", RowBox[List["MathieuS", "[", RowBox[List["a", ",", "q", ",", "0"]], "]"]]]], "-", RowBox[List[RowBox[List["MathieuC", "[", RowBox[List["a", ",", "q", ",", "0"]], "]"]], " ", RowBox[List["MathieuSPrime", "[", RowBox[List["a", ",", "q", ",", "0"]], "]"]]]]]], ")"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|