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ArcSech




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSech[z] > Representations through more general functions > Through Meijer G > Classical cases for the direct function itself





http://functions.wolfram.com/01.30.26.0027.01









  


  








Input Form





ArcSech[Sqrt[z]] - (Pi Sqrt[1/z - 1])/(2 Sqrt[1 - 1/z]) + (Sqrt[1/z - 1]/Sqrt[1 - 1/z]) Sum[(Pochhammer[1/2, k] z^(-k - 1/2))/ ((2 k + 1) k!), {k, 0, n}] == (((-1)^(n - 1) Sqrt[-z^(-1)])/(2 Sqrt[Pi] Sqrt[1/z])) (Sqrt[1/z - 1]/Sqrt[1 - 1/z]) MeijerG[{{1, 1, n + 3/2}, {}}, {{n + 3/2}, {0, 1/2}}, -(1/z)] /; Element[n, Integers] && n >= 0 && !IntervalMemberQ[Interval[{-Infinity, 0}], z]








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["ArcSech", "[", SqrtBox["z_"], "]"]], "-", FractionBox[RowBox[List["\[Pi]", " ", SqrtBox[RowBox[List[FractionBox["1", "z_"], "-", "1"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", "z_"]]]]]]], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "z_"], "-", "1"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "0"]], "n_"], FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "k_"]], "]"]], " ", SuperscriptBox["z_", RowBox[List[RowBox[List["-", "k_"]], "-", FractionBox["1", "2"]]]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k_"]], "+", "1"]], ")"]], " ", RowBox[List["k_", "!"]]]]]]]]], SqrtBox[RowBox[List["1", "-", FractionBox["1", "z_"]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["n", "-", "1"]]], " ", SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]]]], ")"]], " ", SqrtBox[RowBox[List[FractionBox["1", "z"], "-", "1"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", RowBox[List["n", "+", FractionBox["3", "2"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["n", "+", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"]]], "}"]]]], "}"]], ",", RowBox[List["-", FractionBox["1", "z"]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SqrtBox[FractionBox["1", "z"]]]], ")"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", "z"]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]], "&&", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]]]


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





2003-08-21