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variants of this functions
KelvinKei




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.19.06.0005.01









  


  








Input Form





KelvinKei[\[Nu], z] == (-(1/4)) Sum[(1/k!) MeijerG[{{-(k/4), (1 - k)/4, (2 - k)/4, (3 - k)/4}, {(2 \[Nu] - k)/4}}, {{(\[Nu] + k - n)/4, (\[Nu] - k)/4, (2 - \[Nu] - k)/4, -((\[Nu] + k)/4)}, {(2 \[Nu] - k)/4, 0, 1/4, 1/2, 3/4}}, Subscript[z, 0]/4, 1/4] (z - Subscript[z, 0])^k, {k, 0, Infinity}] /; Abs[Arg[Subscript[z, 0]]] < Pi








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["k", "4"]]], ",", FractionBox[RowBox[List["1", "-", "k"]], "4"], ",", FractionBox[RowBox[List["2", "-", "k"]], "4"], ",", FractionBox[RowBox[List["3", "-", "k"]], "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "-", "k"]], ")"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["\[Nu]", "+", "k", "-", "n"]], ")"]]]], ",", FractionBox[RowBox[List["\[Nu]", "-", "k"]], "4"], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["2", "-", "\[Nu]", "-", "k"]], ")"]]]], ",", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List["(", RowBox[List["\[Nu]", "+", "k"]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "-", "k"]], ")"]]]], ",", "0", ",", FractionBox["1", "4"], ",", FractionBox["1", "2"], ",", FractionBox["3", "4"]]], "}"]]]], "}"]], ",", FractionBox[SubscriptBox["zz", "0"], "4"], ",", FractionBox["1", "4"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "k"]]], RowBox[List["k", "!"]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", SubscriptBox["zz", "0"], "]"]], "]"]], "<", "\[Pi]"]]]]]]]]


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





2007-05-02