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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Representations through more general functions > Through Meijer G > Classical cases involving csch-1 in the arguments





http://functions.wolfram.com/01.20.26.0011.01









  


  










Input Form





(1/Sqrt[1 + z]) Cosh[\[Nu] ArcCsch[Sqrt[z]]] == (Cos[(Pi \[Nu])/2]/Sqrt[Pi]) MeijerG[{{1/2}, {0}}, {{\[Nu]/2, -(\[Nu]/2)}, {}}, z] /; !IntervalMemberQ[Interval[{-Infinity, -1}], z]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[RowBox[List["Cosh", "[", RowBox[List["\[Nu]_", " ", RowBox[List["ArcCsch", "[", SqrtBox["z_"], "]"]]]], "]"]], SqrtBox[RowBox[List["1", "+", "z_"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Cos", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "2"], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", "0", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["\[Nu]", "2"], ",", RowBox[List["-", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]]]], SqrtBox["\[Pi]"]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]










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





2001-10-29