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BesselJ






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselJ[nu,z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself





http://functions.wolfram.com/03.01.13.0029.01









  


  










Input Form





Derivative[4][w][z] - (m^4 w[z])/z^2 == 0 /; w[z] == Subscript[c, 1] z (BesselI[2, 2 m Sqrt[z]] - BesselJ[2, 2 m Sqrt[z]]) + Subscript[c, 2] z (BesselI[2, 2 m Sqrt[z]] + BesselJ[2, 2 m Sqrt[z]]) + Subscript[c, 3] MeijerG[{{}, {}}, {{0, 1}, {1/2, 3/2}}, (m^4 z^2)/16] + Subscript[c, 4] MeijerG[{{}, {}}, {{1/2, 3/2}, {0, 1}}, (m^4 z^2)/16]










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["w", TagBox[RowBox[List["(", "4", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z_", "]"]], "-", FractionBox[RowBox[List[SuperscriptBox["m_", "4"], " ", RowBox[List["w", "[", "z_", "]"]]]], SuperscriptBox["z_", "2"]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[SubscriptBox["c", "1"], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["BesselI", "[", RowBox[List["2", ",", RowBox[List["2", " ", "m", " ", SqrtBox["z"]]]]], "]"]], "-", RowBox[List["BesselJ", "[", RowBox[List["2", ",", RowBox[List["2", " ", "m", " ", SqrtBox["z"]]]]], "]"]]]], ")"]]]], "+", RowBox[List[SubscriptBox["c", "2"], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["BesselI", "[", RowBox[List["2", ",", RowBox[List["2", " ", "m", " ", SqrtBox["z"]]]]], "]"]], "+", RowBox[List["BesselJ", "[", RowBox[List["2", ",", RowBox[List["2", " ", "m", " ", SqrtBox["z"]]]]], "]"]]]], ")"]]]], "+", RowBox[List[SubscriptBox["c", "3"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["3", "2"]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List[SuperscriptBox["m", "4"], " ", SuperscriptBox["z", "2"]]], "16"]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "4"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", "1"]], "}"]]]], "}"]], ",", FractionBox[RowBox[List[SuperscriptBox["m", "4"], " ", SuperscriptBox["z", "2"]]], "16"]]], "]"]]]]]]]]]]]]]]










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





2001-10-29





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