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ArcSech




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSech[z] > Transformations > Transformations and argument simplifications > Argument involving basic arithmetic operations > Involving sech-1(a (b zc)m) > Involving sech-1(a (b zc)m) and sech-1(a bm zm c)





http://functions.wolfram.com/01.30.16.0028.01









  


  








Input Form





ArcSech[a (b z^c)^m] == (Sqrt[1/a/(b z^c)^m - 1]/Sqrt[1 - 1/a/(b z^c)^m]) (Pi/2 - ((b^m z^(m c))/(b z^c)^m) (Pi/2 - (Sqrt[1 - 1/a/(b^m z^(m c))]/Sqrt[1/a/(b^m z^(m c)) - 1]) ArcSech[a b^m z^(m c)])) /; Element[2 m, Integers]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSech", "[", RowBox[List["a_", " ", SuperscriptBox[RowBox[List["(", RowBox[List["b_", " ", SuperscriptBox["z_", "c_"]]], ")"]], "m_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SqrtBox[RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", " ", SuperscriptBox["z", "c"]]], ")"]], RowBox[List["-", "m"]]], "a"], "-", "1"]]], " ", RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["b", "m"], " ", SuperscriptBox["z", RowBox[List["m", " ", "c"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox[RowBox[List[SuperscriptBox["b", RowBox[List["-", "m"]]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "m"]], " ", "c"]]]]], "a"]]]], " ", RowBox[List["ArcSech", "[", RowBox[List["a", " ", SuperscriptBox["b", "m"], " ", SuperscriptBox["z", RowBox[List["m", " ", "c"]]]]], "]"]]]], SqrtBox[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["b", RowBox[List["-", "m"]]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "m"]], " ", "c"]]]]], "a"], "-", "1"]]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["b", " ", SuperscriptBox["z", "c"]]], ")"]], "m"]]]], ")"]]]], SqrtBox[RowBox[List["1", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", " ", SuperscriptBox["z", "c"]]], ")"]], RowBox[List["-", "m"]]], "a"]]]]], "/;", RowBox[List[RowBox[List["2", " ", "m"]], "\[Element]", "Integers"]]]]]]]]


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





2003-08-21