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SphericalBesselJ






Mathematica Notation

Traditional Notation









Bessel-Type Functions > SphericalBesselJ[nu,z] > Series representations > Generalized power series > Expansions on branch cuts > For the function itself





http://functions.wolfram.com/03.21.06.0014.01









  


  










Input Form





SphericalBesselJ[\[Nu], z] == Exp[2 \[Nu] Pi I Floor[Arg[z - x]/(2 Pi)]] Sqrt[2] Pi Sum[Sum[(2^(2 j)/(x^j j!)) HypergeometricPFQRegularized[ {-(j/2), (1 - j)/2}, {1 - j + k, (1 - 2 j)/4, (3 - 2 j)/4}, -(x^2/4)] SphericalBesselJ[j - k + \[Nu], x] (z - x)^k, {j, 0, 2 k}]/2^k, {k, 0, Infinity}] /; Element[x, Reals] && x < 0










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[Nu]", " ", "\[Pi]", " ", "\[ImaginaryI]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", "x"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], " ", SqrtBox["2"], " ", "\[Pi]", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SuperscriptBox["2", RowBox[List["-", "k"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List["2", " ", "k"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["2", " ", "j"]]], " ", SuperscriptBox["x", RowBox[List["-", "j"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["j", "2"]]], ",", FractionBox[RowBox[List["1", "-", "j"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", "j", "+", "k"]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "j"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "j"]]]], ")"]]]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["x", "2"], "4"]]]]], "]"]], " ", RowBox[List["SphericalBesselJ", "[", RowBox[List[RowBox[List["j", "-", "k", "+", "\[Nu]"]], ",", "x"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "x"]], ")"]], "k"]]], RowBox[List["j", "!"]]]]]]]]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["x", "<", "0"]]]]]]]]]]










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





2007-05-02