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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Representations through more general functions > Through hypergeometric functions > Involving pFq





http://functions.wolfram.com/01.20.26.0085.01









  


  










Input Form





Cosh[z] == (Pi/2 - I z) HypergeometricPFQ[{-(1/2) + (I z)/Pi, -(1/2) + (I z)/Pi, -(1/2) + (I z)/Pi}, {1, 1}, -1] - (2/Pi^2) (Pi/2 - I z)^3 HypergeometricPFQ[{1/2 + (I z)/Pi, 1/2 + (I z)/Pi, 1/2 + (I z)/Pi}, {2, 2}, -1]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Pi]"]]], ",", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Pi]"]]], ",", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Pi]"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", "1"]], "}"]], ",", RowBox[List["-", "1"]]]], "]"]]]], "-", FractionBox[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], ")"]], "3"], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Pi]"]]], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Pi]"]]], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Pi]"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", "2"]], "}"]], ",", RowBox[List["-", "1"]]]], "]"]]]], SuperscriptBox["\[Pi]", "2"]]]]]]]]










Contributed by





Brychkov Yu.A. (2005)










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





2007-05-02





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