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variants of this functions
Hypergeometric1F1Regularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric1F1Regularized[a,b,z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself





http://functions.wolfram.com/07.21.13.0013.01









  


  










Input Form





z^2 Derivative[2][w][z] + (1 - 2 s + r (-1 + b - d z^r)) z Derivative[1][w][z] + (s (r - b r + s) + d r ((-a) r + s) z^r) w[z] == 0 /; w[z] == Subscript[c, 1] z^s Hypergeometric1F1Regularized[a, b, d z^r] + Subscript[c, 2] z^s HypergeometricU[a, b, d 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[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "s_"]], "+", RowBox[List["r_", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "b_", "-", RowBox[List["d_", " ", SuperscriptBox["z_", "r_"]]]]], ")"]]]]]], ")"]], " ", "z_", " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["s_", " ", RowBox[List["(", RowBox[List["r_", "-", RowBox[List["b_", " ", "r_"]], "+", "s_"]], ")"]]]], "+", RowBox[List["d_", " ", "r_", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a_"]], " ", "r_"]], "+", "s_"]], ")"]], " ", SuperscriptBox["z_", "r_"]]]]], ")"]], " ", 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["Hypergeometric1F1Regularized", "[", RowBox[List["a", ",", "b", ",", RowBox[List["d", " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "2"], " ", SuperscriptBox["z", "s"], " ", RowBox[List["HypergeometricU", "[", RowBox[List["a", ",", "b", ",", RowBox[List["d", " ", SuperscriptBox["z", "r"]]]]], "]"]]]]]]]]]]]]]]










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





2007-05-02





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