|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/07.45.20.0005.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
D[WhittakerW[\[Nu], \[Mu], z], z] ==
(1/2 - \[Nu]/z) WhittakerW[\[Nu], \[Mu], z] -
(1/z) WhittakerW[1 + \[Nu], \[Mu], z]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[Nu]", "z"]]], ")"]], " ", RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "z"]], "]"]]]], "-", RowBox[List[FractionBox["1", "z"], RowBox[List["WhittakerW", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", "\[Mu]", ",", "z"]], "]"]]]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mo> ∂ </mo> <mrow> <msub> <semantics> <mi> W </mi> <annotation encoding='Mathematica'> TagBox["W", WhittakerW] </annotation> </semantics> <mrow> <mi> ν </mi> <mo> , </mo> <mi> μ </mi> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <mi> z </mi> </mrow> </mfrac> <mo>  </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <mfrac> <mi> ν </mi> <mi> z </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <semantics> <mi> W </mi> <annotation encoding='Mathematica'> TagBox["W", WhittakerW] </annotation> </semantics> <mrow> <mi> ν </mi> <mo> , </mo> <mi> μ </mi> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <msub> <semantics> <mi> W </mi> <annotation encoding='Mathematica'> TagBox["W", WhittakerW] </annotation> </semantics> <mrow> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mi> μ </mi> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mi> z </mi> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> WhittakerW </ci> <ci> ν </ci> <ci> μ </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> ν </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> WhittakerW </ci> <ci> ν </ci> <ci> μ </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> WhittakerW </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <ci> μ </ci> <ci> z </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[Nu]", "z"]]], ")"]], " ", RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "z"]], "]"]]]], "-", FractionBox[RowBox[List["WhittakerW", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]"]], ",", "\[Mu]", ",", "z"]], "]"]], "z"]]]]]]] |
|
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
){kind=small}
