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WhittakerM




Mathematica Notation

Traditional Notation









Hypergeometric Functions > WhittakerM[nu,mu,z] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/07.44.20.0011.01









  


  








Input Form





D[WhittakerM[\[Nu], \[Mu], z], {z, n}] == Sum[KroneckerDelta[n, Subscript[k, 1] + Subscript[k, 2] + Subscript[k, 3]] Multinomial[Subscript[k, 1], Subscript[k, 2], Subscript[k, 3]] (-(1/2))^Subscript[k, 1] z^(-Subscript[k, 2] - Subscript[k, 3]/2) (Pochhammer[3/2 - Subscript[k, 2] + \[Mu], Subscript[k, 2]]/ Pochhammer[1 + 2 \[Mu], Subscript[k, 3]]) Pochhammer[1/2 + \[Mu] - \[Nu], Subscript[k, 3]] WhittakerM[-(Subscript[k, 3]/2) + \[Nu], Subscript[k, 3]/2 + \[Mu], z], {Subscript[k, 1], 0, n}, {Subscript[k, 2], 0, n}, {Subscript[k, 3], 0, n}] /; Element[n, Integers] && n >= 0








Standard Form





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MathML Form







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</mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mi> &#956; </mi> <mo> - </mo> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <msub> <mi> k </mi> <mn> 3 </mn> </msub> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;\[Mu]&quot;, &quot;-&quot;, &quot;\[Nu]&quot;, &quot;+&quot;, FractionBox[&quot;1&quot;, &quot;2&quot;]]], &quot;)&quot;]], SubscriptBox[&quot;k&quot;, &quot;3&quot;]], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> M </mi> <annotation encoding='Mathematica'> TagBox[&quot;M&quot;, WhittakerM] </annotation> </semantics> <mrow> <mrow> <mi> &#957; </mi> <mo> - </mo> <mfrac> <msub> <mi> k </mi> <mn> 3 </mn> </msub> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mi> &#956; </mi> <mo> + </mo> <mfrac> <msub> <mi> k </mi> <mn> 3 </mn> </msub> <mn> 2 </mn> </mfrac> </mrow> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; 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</ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> k </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <ci> WhittakerM </ci> <apply> <plus /> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> k </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> &#956; </ci> <apply> <times /> <apply> <ci> Subscript </ci> <ci> k </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "n_"]], "}"]]]]], RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["k", "1"], "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["k", "2"], "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["k", "3"], "=", "0"]], "n"], FractionBox[RowBox[List[RowBox[List["KroneckerDelta", "[", RowBox[List["n", ",", RowBox[List[SubscriptBox["k", "1"], "+", SubscriptBox["k", "2"], "+", SubscriptBox["k", "3"]]]]], "]"]], " ", RowBox[List["Multinomial", "[", RowBox[List[SubscriptBox["k", "1"], ",", SubscriptBox["k", "2"], ",", SubscriptBox["k", "3"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["1", "2"]]], ")"]], SubscriptBox["k", "1"]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", SubscriptBox["k", "2"]]], "-", FractionBox[SubscriptBox["k", "3"], "2"]]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[FractionBox["3", "2"], "-", SubscriptBox["k", "2"], "+", "\[Mu]"]], ",", SubscriptBox["k", "2"]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ",", SubscriptBox["k", "3"]]], "]"]], " ", RowBox[List["WhittakerM", "[", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[SubscriptBox["k", "3"], "2"]]], "+", "\[Nu]"]], ",", RowBox[List[FractionBox[SubscriptBox["k", "3"], "2"], "+", "\[Mu]"]], ",", "z"]], "]"]]]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]], ",", SubscriptBox["k", "3"]]], "]"]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]


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





2007-05-02