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SphericalBesselJ






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.21.13.0005.01









  


  










Input Form





4 z^2 Derivative[2][w][z] + 4 z (1 - 2 p + q) Derivative[1][w][z] + (4 p^2 - 4 p q + q^2 (1 + 4 m^2 z^(2 q) - 4 \[Nu]^2)) w[z] == 0 /; w[z] == Subscript[c, 1] z^p SphericalBesselJ[\[Nu], m z^q] + Subscript[c, 2] z^p SphericalBesselY[\[Nu], m z^q]










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["4", " ", SuperscriptBox["z_", "2"], " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "+", RowBox[List["4", " ", "z_", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "p_"]], "+", "q_"]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["4", " ", SuperscriptBox["p_", "2"]]], "-", RowBox[List["4", " ", "p_", " ", "q_"]], "+", RowBox[List[SuperscriptBox["q_", "2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", SuperscriptBox["m_", "2"], " ", SuperscriptBox["z_", RowBox[List["2", " ", "q_"]]]]], "-", RowBox[List["4", " ", SuperscriptBox["\[Nu]_", "2"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["w", "[", "z_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[SubscriptBox["c", "1"], " ", SuperscriptBox["z", "p"], " ", RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]", ",", RowBox[List["m", " ", SuperscriptBox["z", "q"]]]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "2"], " ", SuperscriptBox["z", "p"], " ", RowBox[List["SphericalBesselY", "[", RowBox[List["\[Nu]", ",", RowBox[List["m", " ", SuperscriptBox["z", "q"]]]]], "]"]]]]]]]]]]]]]]










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





2007-05-02