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variants of this functions
KelvinBei






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinBei[z] > Series representations > Generalized power series > Expansions at generic point z==z0





http://functions.wolfram.com/03.13.06.0004.01









  


  










Input Form





KelvinBei[z] == ((I Sqrt[Pi])/2) Sum[((2^k/k!) (HypergeometricPFQRegularized[{1/2}, {(1 - k)/2, (2 - k)/2}, -((I Subscript[z, 0]^2)/4)] - HypergeometricPFQRegularized[{1/2}, {(1 - k)/2, (2 - k)/2}, (I Subscript[z, 0]^2)/4]) (z - Subscript[z, 0])^k)/Subscript[z, 0]^k, {k, 0, Infinity}]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinBei", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SqrtBox["\[Pi]"]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox["2", "k"], " ", RowBox[List["(", RowBox[List[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "k"]], "2"], ",", FractionBox[RowBox[List["2", "-", "k"]], "2"]]], "}"]], ",", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SubsuperscriptBox["zz", "0", "2"]]], ")"]]]]]], "]"]], "-", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "k"]], "2"], ",", FractionBox[RowBox[List["2", "-", "k"]], "2"]]], "}"]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SubsuperscriptBox["zz", "0", "2"]]], "4"]]], "]"]]]], ")"]], " ", SubsuperscriptBox["zz", "0", RowBox[List["-", "k"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "k"]]], RowBox[List["k", "!"]]]]]]]]]]]










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





2007-05-02