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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Series representations > Generalized power series > Expansions at z==Pi/2 > For the function itself





http://functions.wolfram.com/01.07.06.0049.01









  


  








Input Form





Cos[z] == Subscript[F, Infinity][z] /; Subscript[F, n][z] == (-(z - Pi/2)) Sum[((-1)^k/(2^(2 k) k! Pochhammer[3/2, k])) (z - Pi/2)^(2 k), {k, 0, n}] == Cos[z] + ((-1)^n/(3 + 2 n)!) (Pi/2 - z)^(3 + 2 n) HypergeometricPFQ[{1}, {2 + n, 5/2 + n}, (-(1/4)) (Pi/2 - z)^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", "[", RowBox[List["Cos", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubscriptBox["F", "\[Infinity]"], "[", "z", "]"]], "/;", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["F", "n"], "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["z", "-", FractionBox["\[Pi]", "2"]]], ")"]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", FractionBox["\[Pi]", "2"]]], ")"]], RowBox[List["2", " ", "k"]]]]], RowBox[List[SuperscriptBox["2", RowBox[List["2", " ", "k"]]], " ", RowBox[List["k", "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", "k"]], "]"]]]]]]]]], "\[Equal]", RowBox[List[RowBox[List["Cos", "[", "z", "]"]], "+", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", "z"]], ")"]], RowBox[List["3", "+", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "+", "n"]], ",", RowBox[List[FractionBox["5", "2"], "+", "n"]]]], "}"]], ",", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", "z"]], ")"]], "2"]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "n"]]]], ")"]], "!"]]]]]]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]


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





2007-05-02