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 ChebyshevU

 http://functions.wolfram.com/07.05.20.0001.01

 Input Form

 D[ChebyshevU[\[Nu], z], \[Nu]] == (ArcCos[z]/Sqrt[1 - z^2]) ChebyshevT[\[Nu] + 1, z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "\[Nu]"], RowBox[List["ChebyshevU", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["ArcCos", "[", "z", "]"]], SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]], RowBox[List["ChebyshevT", "[", RowBox[List[RowBox[List["\[Nu]", "+", "1"]], ",", "z"]], "]"]]]]]]]]

 MathML Form

 U ν ( z ) ν cos - 1 ( z ) 1 - z 2 T ν + 1 ( z ) ν ChebyshevU ν z z 1 -1 z 2 1 2 -1 ChebyshevT ν 1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["\[Nu]_"]]], RowBox[List["ChebyshevU", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["ArcCos", "[", "z", "]"]], " ", RowBox[List["ChebyshevT", "[", RowBox[List[RowBox[List["\[Nu]", "+", "1"]], ",", "z"]], "]"]]]], SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]]]]

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

 2001-10-29