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Sinh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.19.26.0030.01









  


  










Input Form





Sinh[z]^n == (-1)^(n/2) 2^(-n - 1) Binomial[n, n/2] ((-1)^n + 1) + 2^(1 - n) Pi^(3/2) Sum[(-1)^(k + n) Binomial[n, k] MeijerG[{{}, {(1/4) (1 + (-1)^n)}}, {{(1/4) (1 - (-1)^n)}, {(1/4) (1 + (-1)^n), (1/4) (1 + (-1)^n)}}, (1/2) z (n - 2 k), 1/2], {k, 0, Floor[(n - 1)/2]}] /; 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["Sinh", "[", "z_", "]"]], "n_"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["n", "/", "2"]]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "n"]], "-", "1"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", FractionBox["n", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], "+", "1"]], ")"]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "n"]]], " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["k", "+", "n"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "k"]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"]]], ")"]]]]]], "}"]]]], "}"]], ",", RowBox[List[FractionBox["1", "2"], " ", "z", " ", RowBox[List["(", RowBox[List["n", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], ",", FractionBox["1", "2"]]], "]"]]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]










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





2001-10-29