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variants of this functions
KelvinBei




Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinBei[nu,z] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/03.17.20.0020.01









  


  








Input Form





D[KelvinBei[\[Nu], z], {z, \[Alpha]}] == ((2^(-\[Nu] - 1) I z^(-\[Alpha] + \[Nu]))/Gamma[1 - \[Alpha] + \[Nu]]) (HypergeometricPFQ[{(\[Nu] + 1)/2, 1 + \[Nu]/2}, {(\[Nu] - \[Alpha] + 1)/2, 1 + (\[Nu] - \[Alpha])/2, 1 + \[Nu]}, -((I z^2)/4)]/ E^((3/4) I Pi \[Nu]) - E^((3 I Pi \[Nu])/4) HypergeometricPFQ[ {(\[Nu] + 1)/2, 1 + \[Nu]/2}, {(\[Nu] - \[Alpha] + 1)/2, 1 + (\[Nu] - \[Alpha])/2, 1 + \[Nu]}, (I z^2)/4])








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["KelvinBei", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "1"]]], " ", "\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "\[Alpha]"]], "+", "\[Nu]"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["-", "3"]], ")"]], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["\[Nu]", "+", "1"]], "2"], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["\[Nu]", "-", "\[Alpha]", "+", "1"]], ")"]]]], ",", RowBox[List["1", "+", FractionBox[RowBox[List["\[Nu]", "-", "\[Alpha]"]], "2"]]], ",", RowBox[List["1", "+", "\[Nu]"]]]], "}"]], ",", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]], ")"]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "4"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["\[Nu]", "+", "1"]], "2"], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["\[Nu]", "-", "\[Alpha]", "+", "1"]], ")"]]]], ",", RowBox[List["1", "+", FractionBox[RowBox[List["\[Nu]", "-", "\[Alpha]"]], "2"]]], ",", RowBox[List["1", "+", "\[Nu]"]]]], "}"]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]], "4"]]], "]"]]]]]], ")"]]]], RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Alpha]", "+", "\[Nu]"]], "]"]]]]]]]


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





2007-05-02