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variants of this functions
KelvinBer






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinBer[nu,z] > Representations through more general functions > Through Meijer G > Classical cases involving bei





http://functions.wolfram.com/03.18.26.0016.01









  


  










Input Form





KelvinBer[\[Mu], z^(1/4)] KelvinBer[\[Nu], z^(1/4)] - KelvinBei[\[Nu], z^(1/4)] KelvinBei[\[Mu], z^(1/4)] == 2^(3/2) Pi^(5/2) MeijerG[{{0, 1/4, 3/4}, {1/6, 1/2, 5/6}}, {{(\[Mu] + \[Nu])/4, (\[Mu] + \[Nu] + 2)/4}, {1/6, 5/6, -((\[Mu] + \[Nu])/4), (\[Mu] - \[Nu])/4, (\[Nu] - \[Mu])/4, (2 - \[Mu] - \[Nu])/4, (\[Mu] - \[Nu] + 2)/4, (\[Nu] - \[Mu] + 2)/4}}, z/16]










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[RowBox[List["KelvinBer", "[", RowBox[List["\[Mu]_", ",", SuperscriptBox["z_", RowBox[List["1", "/", "4"]]]]], "]"]], " ", RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]_", ",", SuperscriptBox["z_", RowBox[List["1", "/", "4"]]]]], "]"]]]], "-", RowBox[List[RowBox[List["KelvinBei", "[", RowBox[List["\[Nu]_", ",", SuperscriptBox["z_", RowBox[List["1", "/", "4"]]]]], "]"]], " ", RowBox[List["KelvinBei", "[", RowBox[List["\[Mu]_", ",", SuperscriptBox["z_", RowBox[List["1", "/", "4"]]]]], "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["\[Pi]", RowBox[List["5", "/", "2"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "4"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "6"], ",", FractionBox["1", "2"], ",", FractionBox["5", "6"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["\[Mu]", "+", "\[Nu]"]], "4"], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["\[Mu]", "+", "\[Nu]", "+", "2"]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "6"], ",", FractionBox["5", "6"], ",", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List["(", RowBox[List["\[Mu]", "+", "\[Nu]"]], ")"]]]], ",", FractionBox[RowBox[List["\[Mu]", "-", "\[Nu]"]], "4"], ",", FractionBox[RowBox[List["\[Nu]", "-", "\[Mu]"]], "4"], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["2", "-", "\[Mu]", "-", "\[Nu]"]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["\[Mu]", "-", "\[Nu]", "+", "2"]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["\[Nu]", "-", "\[Mu]", "+", "2"]], ")"]]]]]], "}"]]]], "}"]], ",", FractionBox["z", "16"]]], "]"]]]]]]]]










Contributed by





Brychkov Yu.A. (2006)










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





2007-05-02





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