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variants of this functions
ChebyshevU






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevU[nu,z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself > With respect to z





http://functions.wolfram.com/07.05.13.0022.01









  


  










Input Form





z^2 (-1 + a^2 z^(2 r)) Derivative[2][w][z] + (-1 + r + 2 s + a^2 (1 + 2 r - 2 s) z^(2 r)) z Derivative[1][w][z] + ((-s) (r + s) + a^2 z^(2 r) (s + r \[Nu]) (s - r (2 + \[Nu]))) w[z] == 0 /; w[z] == Subscript[c, 1] z^s ChebyshevU[\[Nu], a z^r] + Subscript[c, 2] (z^s/Sqrt[1 - a^2 z^(2 r)]) ChebyshevT[\[Nu] + 1, a z^r]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SuperscriptBox["z_", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[SuperscriptBox["a_", "2"], " ", SuperscriptBox["z_", RowBox[List["2", " ", "r_"]]]]]]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "r_", "+", RowBox[List["2", " ", "s_"]], "+", RowBox[List[SuperscriptBox["a_", "2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "r_"]], "-", RowBox[List["2", " ", "s_"]]]], ")"]], " ", SuperscriptBox["z_", RowBox[List["2", " ", "r_"]]]]]]], ")"]], " ", "z_", " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "s_"]], " ", RowBox[List["(", RowBox[List["r_", "+", "s_"]], ")"]]]], "+", RowBox[List[SuperscriptBox["a_", "2"], " ", SuperscriptBox["z_", RowBox[List["2", " ", "r_"]]], " ", RowBox[List["(", RowBox[List["s_", "+", RowBox[List["r_", " ", "\[Nu]_"]]]], ")"]], " ", RowBox[List["(", RowBox[List["s_", "-", RowBox[List["r_", " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]_"]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["w", "[", "z_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[SubscriptBox["c", "1"], " ", SuperscriptBox["z", "s"], " ", RowBox[List["ChebyshevU", "[", RowBox[List["\[Nu]", ",", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", FractionBox[RowBox[List[SubscriptBox["c", "2"], " ", SuperscriptBox["z", "s"], " ", RowBox[List["ChebyshevT", "[", RowBox[List[RowBox[List["\[Nu]", "+", "1"]], ",", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]], "]"]]]], SqrtBox[RowBox[List["1", "-", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", RowBox[List["2", " ", "r"]]]]]]]]]]]]]]]]]]]










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





2007-05-02





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