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http://functions.wolfram.com/04.11.27.0004.01
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Fibonacci[\[Nu]] == ((1/Sqrt[5]) (E^(2 \[Nu] ArcCsch[2]) - Cos[Pi \[Nu]]))/
E^(\[Nu] ArcCsch[2])
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Cell[BoxData[RowBox[List[RowBox[List["Fibonacci", "[", "\[Nu]", "]"]], "\[Equal]", RowBox[List[FractionBox["1", SqrtBox["5"]], SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[Nu]"]], " ", RowBox[List["ArcCsch", "[", "2", "]"]]]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[Nu]", " ", RowBox[List["ArcCsch", "[", "2", "]"]]]]], "-", RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], ")"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msub> <semantics> <mi> F </mi> <annotation encoding='Mathematica'> TagBox["F", Fibonacci] </annotation> </semantics> <mi> ν </mi> </msub> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <msqrt> <mn> 5 </mn> </msqrt> </mfrac> <mo> ⁢ </mo> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> csch </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> csch </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Fibonacci </ci> <ci> ν </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <exp /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <apply> <arccsch /> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <exp /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> <apply> <arccsch /> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <cos /> <apply> <times /> <pi /> <ci> ν </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Fibonacci", "[", "\[Nu]_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[Nu]"]], " ", RowBox[List["ArcCsch", "[", "2", "]"]]]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[Nu]", " ", RowBox[List["ArcCsch", "[", "2", "]"]]]]], "-", RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], ")"]]]], SqrtBox["5"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
