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 GoldenRatio

 http://functions.wolfram.com/02.02.09.0002.01

 Input Form

 GoldenRatio == Limit[Subscript[z, n], n -> Infinity] /; Subscript[z, n + 1] == Sqrt[1 + Subscript[z, n]] && Subscript[z, 0] == 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["GoldenRatio", "\[Equal]", RowBox[List["Limit", "[", RowBox[List[SubscriptBox["z", "n"], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["z", RowBox[List["n", "+", "1"]]], "\[Equal]", SqrtBox[RowBox[List["1", "+", SubscriptBox["z", "n"]]]]]], "\[And]", RowBox[List[SubscriptBox["z", "0"], "\[Equal]", "1"]]]]]]]]

 MathML Form

 ϕ TagBox["\[Phi]", Function[GoldenRatio]] lim n "\[Rule]" z n /; z n + 1 = 1 + z n z 0 1 Set Condition GoldenRatio n n Subscript z n Subscript z n 1 1 Subscript z n 1 2 Subscript z 0 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "GoldenRatio", "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Limit", "[", RowBox[List[SubscriptBox["z", "n"], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]], "/;", RowBox[List[RowBox[List[SubscriptBox["z", RowBox[List["n", "+", "1"]]], "\[Equal]", SqrtBox[RowBox[List["1", "+", SubscriptBox["z", "n"]]]]]], "&&", RowBox[List[SubscriptBox["z", "0"], "\[Equal]", "1"]]]]]]]]]]

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

 2001-10-29