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Sech




Mathematica Notation

Traditional Notation









Elementary Functions > Sech[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving powers of the direct function and hyperbolic functions > Involving power of coth > Involving cothmu(c z) sechnu(c z)





http://functions.wolfram.com/01.24.21.0423.01









  


  








Input Form





Integrate[Coth[c z]^\[Mu] Sech[c z]^\[Nu], z] == (-(1/(c (1 + \[Mu] - \[Nu])))) Coth[c z]^\[Mu] Sech[c z]^(-1 + \[Nu]) Sinh[c z] (-Sinh[c z]^2)^((1/2) (-1 + \[Mu])) Hypergeometric2F1[(1/2) (1 + \[Mu] - \[Nu]), (1 + \[Mu])/2, (1/2) (3 + \[Mu] - \[Nu]), Cosh[c z]^2]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Coth", "[", RowBox[List["c_", " ", "z_"]], "]"]], "\[Mu]_"], " ", SuperscriptBox[RowBox[List["Sech", "[", RowBox[List["c_", " ", "z_"]], "]"]], "\[Nu]_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["Coth", "[", RowBox[List["c", " ", "z"]], "]"]], "\[Mu]"], " ", SuperscriptBox[RowBox[List["Sech", "[", RowBox[List["c", " ", "z"]], "]"]], RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]]], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[Mu]"]], ")"]]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "\[Mu]", "-", "\[Nu]"]], ")"]]]], ",", FractionBox[RowBox[List["1", "+", "\[Mu]"]], "2"], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["3", "+", "\[Mu]", "-", "\[Nu]"]], ")"]]]], ",", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]], "]"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["1", "+", "\[Mu]", "-", "\[Nu]"]], ")"]]]]]]]]]]]


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





2002-12-18