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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Specific values > Values at fixed points





http://functions.wolfram.com/01.19.03.0013.01









  


  










Input Form





Sinh[(Pi I)/7] == (1/24) (-4 I Sqrt[7] + (2 Sqrt[7] (I + Sqrt[3]))/ (7 - (I Sqrt[7])/2 - (3 Sqrt[21])/2)^(1/3) + (2 + 2 I Sqrt[3]) (7 - (I Sqrt[7])/2 - (3 Sqrt[21])/2)^(1/3) - (2 Sqrt[7] (-I + Sqrt[3]))/(7 + (I Sqrt[7])/2 + (3 Sqrt[21])/2)^(1/3) + 2 I (I + Sqrt[3]) (7 + (I Sqrt[7])/2 + (3 Sqrt[21])/2)^(1/3))










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sinh", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "7"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "24"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "\[ImaginaryI]", " ", SqrtBox["7"]]], "+", FractionBox[RowBox[List["2", " ", SqrtBox["7"], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["7", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "2"], "-", FractionBox[RowBox[List["3", " ", SqrtBox["21"]]], "2"]]], ")"]], RowBox[List["1", "/", "3"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["7", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "2"], "-", FractionBox[RowBox[List["3", " ", SqrtBox["21"]]], "2"]]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", FractionBox[RowBox[List["2", " ", SqrtBox["7"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["7", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "2"], "+", FractionBox[RowBox[List["3", " ", SqrtBox["21"]]], "2"]]], ")"]], RowBox[List["1", "/", "3"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["7", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "2"], "+", FractionBox[RowBox[List["3", " ", SqrtBox["21"]]], "2"]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]]]]]]]]










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





2001-10-29