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ArcSech






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.30.26.0032.01









  


  










Input Form





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










Standard Form





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MathML Form







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</ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["ArcSech", "[", "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[RowBox[List["-", "2"]], " ", "k_"]], "-", "1"]]]]], 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[FractionBox["1", "2"], "+", "n"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", FractionBox["1", "z"]]]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "n"]], "-", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", FractionBox["1", "2"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "0", ",", RowBox[List[RowBox[List["-", "n"]], "-", FractionBox["1", "2"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]], ",", FractionBox["1", "2"]]], "]"]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", "z"]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]










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





2007-05-02





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