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variants of this functions
KelvinBei






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinBei[nu,z] > Limit representations





http://functions.wolfram.com/03.17.09.0003.01









  


  










Input Form





KelvinBei[\[Nu], z] == (1/Gamma[\[Nu] + 1]) (z/2)^\[Nu] Limit[Sin[(3 Pi \[Nu])/4] HypergeometricPFQ[{a}, {1/2, (\[Nu] + 1)/2, \[Nu]/2 + 1}, -(z^4/(256 a))] + ((Cos[(3 Pi \[Nu])/4] z^2)/(4 (\[Nu] + 1))) HypergeometricPFQ[{a}, {3/2, (\[Nu] + 3)/2, \[Nu]/2 + 1}, -(z^4/(256 a))], a -> 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", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], "\[Nu]"], " ", RowBox[List["Limit", "[", RowBox[List[RowBox[List[RowBox[List[RowBox[List["Sin", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "4"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "a", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox[RowBox[List["\[Nu]", "+", "1"]], "2"], ",", RowBox[List[FractionBox["\[Nu]", "2"], "+", "1"]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], RowBox[List["256", " ", "a"]]]]]]], "]"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Cos", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "4"], "]"]], " ", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "a", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox[RowBox[List["\[Nu]", "+", "3"]], "2"], ",", RowBox[List[FractionBox["\[Nu]", "2"], "+", "1"]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], RowBox[List["256", " ", "a"]]]]]]], "]"]]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List["\[Nu]", "+", "1"]], ")"]]]]]]], ",", RowBox[List["a", "\[Rule]", "\[Infinity]"]]]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]]]]]]]










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





2007-05-02





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