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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Series representations > Generalized power series > Expansions at z==0 > For powers of the function > For symbolical integer power





http://functions.wolfram.com/01.20.06.0042.01









  


  










Input Form





Cosh[z]^n == (Binomial[n, n/2] (1 - Mod[n, 2]))/2^n + 2^(1 - n) Sum[Binomial[n, k] Hypergeometric0F1[1/2, ((n - 2 k)^2 z^2)/4], {k, 0, Floor[(n - 1)/2]}] /; Element[n, Integers] && n > 0










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["Cosh", "[", "z_", "]"]], "n_"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["-", "n"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", FractionBox["n", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["n", ",", "2"]], "]"]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["n", ",", "k"]], "]"]], " ", RowBox[List["Hypergeometric0F1", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["n", "-", RowBox[List["2", " ", "k"]]]], ")"]], "2"], " ", SuperscriptBox["z", "2"]]]]], "]"]]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]










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





2007-05-02