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ArcCsch




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsch[z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself





http://functions.wolfram.com/01.29.06.0037.01









  


  








Input Form





ArcCsch[z] == Subscript[F, Infinity][z] /; Subscript[F, n][z] == (z/2) Sqrt[1/z^2] Log[4/z^2] + (z^3/4) Sqrt[1/z^2] Sum[((-1)^k Pochhammer[3/2, k] z^(2 k))/ ((1 + k)^2 k!), {k, 0, n}] == ArcCsch[z] + Sqrt[1/z^2] (((-1)^n z^(5 + 2 n) Pochhammer[3/2, 1 + n])/ (4 (n + 2) (n + 2)!)) HypergeometricPFQ[{1, n + 5/2, n + 2, n + 2}, {n + 2, n + 3, n + 3}, -z^2] && 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["ArcCsch", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubscriptBox["F", "\[Infinity]"], "[", "z", "]"]], "/;", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["F", "n"], "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "z", " ", SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], " ", RowBox[List["Log", "[", FractionBox["4", SuperscriptBox["z", "2"]], "]"]]]], "+", RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox["z", "3"], " ", SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", "k"]], "]"]], " ", SuperscriptBox["z", RowBox[List["2", " ", "k"]]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "k"]], ")"]], "2"], " ", RowBox[List["k", "!"]]]]]]]]]]], "\[Equal]", RowBox[List[RowBox[List["ArcCsch", "[", "z", "]"]], "+", FractionBox[RowBox[List[SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", SuperscriptBox["z", RowBox[List["5", "+", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["1", "+", "n"]]]], "]"]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List["n", "+", FractionBox["5", "2"]]], ",", RowBox[List["n", "+", "2"]], ",", RowBox[List["n", "+", "2"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["n", "+", "2"]], ",", RowBox[List["n", "+", "3"]], ",", RowBox[List["n", "+", "3"]]]], "}"]], ",", RowBox[List["-", SuperscriptBox["z", "2"]]]]], "]"]]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List["n", "+", "2"]], ")"]], " ", RowBox[List[RowBox[List["(", RowBox[List["n", "+", "2"]], ")"]], "!"]]]]]]]]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]


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





2007-05-02