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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Representations through more general functions > Through Meijer G > Generalized cases for powers of cosh





http://functions.wolfram.com/01.20.26.0080.01









  


  








Input Form





Cosh[z]^(2 n) == 1 - 2^(1 - 2 n) Pi^(3/2) Sum[Binomial[2 n, k] MeijerG[{{1}, {1/2}}, {{1}, {0, 1/2, 1/2}}, (-k + n) z, 1/2], {k, 0, n - 1}] /; Element[n, Integers] && n >= 0








Standard Form





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MathML Form







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</ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["Cosh", "[", "z_", "]"]], RowBox[List["2", " ", "n_"]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["1", "-", RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["n", "-", "1"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List["2", " ", "n"]], ",", "k"]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"], ",", FractionBox["1", "2"]]], "}"]]]], "}"]], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "k"]], "+", "n"]], ")"]], " ", "z"]], ",", FractionBox["1", "2"]]], "]"]]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]


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





2003-08-21