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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 z==0 > For the function itself





http://functions.wolfram.com/03.13.06.0011.01









  


  










Input Form





KelvinBei[z] == Subscript[F, Infinity][z] /; Subscript[F, n][z] == (z^2/4) Sum[((-1)^k/(2 k + a)!^2) (z/2)^(4 k), {k, 0, n}] == KelvinBei[z] + (((-1)^n 4^(-3 - 2 n))/Gamma[4 + 2 n]^2) z^(4 n + 6) HypergeometricPFQ[{1}, {2 + n, 2 + n, 5/2 + n, 5/2 + n}, -(z^4/256)] && Element[n, Integers] && n >= 0










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[RowBox[List[SubscriptBox["F", "\[Infinity]"], "[", "z", "]"]], "/;", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["F", "n"], "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox["z", "2"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List["4", " ", "k"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "a"]], ")"]], "!"]], ")"]], "2"]]]]]], "\[Equal]", RowBox[List[RowBox[List["KelvinBei", "[", "z", "]"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", SuperscriptBox["4", RowBox[List[RowBox[List["-", "3"]], "-", RowBox[List["2", " ", "n"]]]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["4", " ", "n"]], "+", "6"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "+", "n"]], ",", RowBox[List["2", "+", "n"]], ",", RowBox[List[FractionBox["5", "2"], "+", "n"]], ",", RowBox[List[FractionBox["5", "2"], "+", "n"]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "256"]]]]], "]"]]]], SuperscriptBox[RowBox[List["Gamma", "[", RowBox[List["4", "+", RowBox[List["2", " ", "n"]]]], "]"]], "2"]]]]]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]










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





2007-05-02