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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 the third power





http://functions.wolfram.com/01.20.06.0038.01









  


  










Input Form





Cosh[z]^3 == Subscript[F, Infinity][z] /; Subscript[F, m][z] == 1 + (1/4) Sum[((3 + 3^(2 j)) z^(2 j))/(2 j)!, {j, 1, m}] == Cosh[z]^3 - 2^(-4 - 2 m) Sqrt[Pi] z^(2 + 2 m) (3^(2 + 2 m) HypergeometricPFQRegularized[{1}, {3/2 + m, 2 + m}, (9 z^2)/4] + 3 HypergeometricPFQRegularized[{1}, {3/2 + m, 2 + m}, z^2/4]) && Element[m, Integers] && m >= 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_", "]"]], "3"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubscriptBox["F", "\[Infinity]"], "[", "z", "]"]], "/;", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["F", "m"], "[", "z", "]"]], "\[Equal]", RowBox[List["1", "+", RowBox[List[FractionBox["1", "4"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], "m"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List["3", "+", SuperscriptBox["3", RowBox[List["2", " ", "j"]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["2", " ", "j"]]]]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", "j"]], ")"]], "!"]]]]]]]]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["Cosh", "[", "z", "]"]], "3"], "-", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "4"]], "-", RowBox[List["2", " ", "m"]]]]], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["2", "+", RowBox[List["2", " ", "m"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["3", RowBox[List["2", "+", RowBox[List["2", " ", "m"]]]]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["3", "2"], "+", "m"]], ",", RowBox[List["2", "+", "m"]]]], "}"]], ",", FractionBox[RowBox[List["9", " ", SuperscriptBox["z", "2"]]], "4"]]], "]"]]]], "+", RowBox[List["3", " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["3", "2"], "+", "m"]], ",", RowBox[List["2", "+", "m"]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "2"], "4"]]], "]"]]]]]], ")"]]]]]]]], "&&", RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", "\[GreaterEqual]", "0"]]]]]]]]]]










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





2007-05-02





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