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ParabolicCylinderD




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ParabolicCylinderD[nu,z] > Identities > Recurrence identities > Consecutive neighbors





http://functions.wolfram.com/07.41.17.0002.01









  


  








Input Form





ParabolicCylinderD[\[Nu], z] == (-z) ParabolicCylinderD[\[Nu] - 1, z] + (\[Nu] - 1) ParabolicCylinderD[\[Nu] - 2, z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["ParabolicCylinderD", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "z"]], " ", RowBox[List["ParabolicCylinderD", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["\[Nu]", "-", "1"]], ")"]], " ", RowBox[List["ParabolicCylinderD", "[", RowBox[List[RowBox[List["\[Nu]", "-", "2"]], ",", "z"]], "]"]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <semantics> <mi> D </mi> <annotation encoding='Mathematica'> TagBox[&quot;D&quot;, ParabolicCylinderD] </annotation> </semantics> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> D </mi> <annotation encoding='Mathematica'> TagBox[&quot;D&quot;, ParabolicCylinderD] </annotation> </semantics> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> D </mi> <annotation encoding='Mathematica'> TagBox[&quot;D&quot;, ParabolicCylinderD] </annotation> </semantics> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> ParabolicCylinderD </ci> <ci> &#957; </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> <apply> <ci> ParabolicCylinderD </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <ci> ParabolicCylinderD </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ParabolicCylinderD", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "z"]], " ", RowBox[List["ParabolicCylinderD", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["\[Nu]", "-", "1"]], ")"]], " ", RowBox[List["ParabolicCylinderD", "[", RowBox[List[RowBox[List["\[Nu]", "-", "2"]], ",", "z"]], "]"]]]]]]]]]]


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





2007-05-02