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http://functions.wolfram.com/04.11.32.0001.01
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Fibonacci[n] == Det[Table[Which[k == l, 1,
Abs[k - l] == 1, I, True, 0], {k, n}, {l, n}]]
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Cell[BoxData[RowBox[List[RowBox[List["Fibonacci", "[", "n", "]"]], "\[Equal]", RowBox[List["Det", "[", RowBox[List["Table", "[", RowBox[List[RowBox[List["Which", "[", RowBox[List[RowBox[List["k", "\[Equal]", "l"]], ",", "1", ",", RowBox[List[RowBox[List["Abs", "[", RowBox[List["k", "-", "l"]], "]"]], "\[Equal]", "1"]], ",", "\[ImaginaryI]", ",", "True", ",", "0"]], "]"]], ",", RowBox[List["{", RowBox[List["k", ",", "n"]], "}"]], ",", RowBox[List["{", RowBox[List["l", ",", "n"]], "}"]]]], "]"]], "]"]]]]]]
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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> n </mi> </msub> <mo> ⩵ </mo> <semantics> <mrow> <mo> ❘ </mo> <msub> <mrow> <mo> ( </mo> <mrow> <mo> { </mo> <mtable> <mtr> <mtd> <mn> 1 </mn> </mtd> <mtd> <mrow> <mrow> <mi> if </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> ⩵ </mo> <mi> l </mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mi> ⅈ </mi> </mtd> <mtd> <mrow> <mrow> <mi> if </mi> <mo> ⁢ </mo> <mrow> <mo> ❘ </mo> <mrow> <mi> k </mi> <mo> - </mo> <mi> l </mi> </mrow> <mo> ❘ </mo> </mrow> </mrow> <mo> ⩵ </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn> 0 </mn> </mtd> <mtd> <mi> else </mi> </mtd> </mtr> </mtable> <mo mathcolor='#FFFFFF'> } </mo> </mrow> <mo> ) </mo> </mrow> <mtable> <mtr> <mtd> <mrow> <mn> 1 </mn> <mo> ≤ </mo> <mi> k </mi> <mo> ≤ </mo> <mi> n </mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 1 </mn> <mo> ≤ </mo> <mi> l </mi> <mo> ≤ </mo> <mi> n </mi> </mrow> </mtd> </mtr> </mtable> </msub> <mo> ❘ </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[LeftBracketingBar]", SubscriptBox[RowBox[List["(", StyleBox[RowBox[List["{", GridBox[List[List["1", RowBox[List[RowBox[List["if", " ", "k"]], "\[Equal]", "l"]]], List["\[ImaginaryI]", RowBox[List[RowBox[List["if", " ", RowBox[List["\[LeftBracketingBar]", RowBox[List["k", "-", "l"]], "\[RightBracketingBar]"]]]], "\[Equal]", "1"]]], List["0", "else"]]], StyleBox["}", Rule[FontColor, GrayLevel[1]]]]], Rule[SpanMaxSize, DirectedInfinity[1]]], ")"]], GridBox[List[List[RowBox[List["1", "\[LessEqual]", "k", "\[LessEqual]", "n"]]], List[RowBox[List["1", "\[LessEqual]", "l", "\[LessEqual]", "n"]]]]]], "\[RightBracketingBar]"]], List[Det]] </annotation> </semantics> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <msub> <semantics> <mi> F </mi> <annotation encoding='Mathematica'> TagBox["F", Fibonacci] </annotation> </semantics> <mi> n </mi> </msub> <mo> ⩵ </mo> <semantics> <mrow> <mo> ❘ </mo> <msub> <mrow> <mo> ( </mo> <mrow> <mo> { </mo> <mtable> <mtr> <mtd> <mn> 1 </mn> </mtd> <mtd> <mrow> <mrow> <mi> if </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> ⩵ </mo> <mi> l </mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mi> ⅈ </mi> </mtd> <mtd> <mrow> <mrow> <mi> if </mi> <mo> ⁢ </mo> <mrow> <mo> ❘ </mo> <mrow> <mi> k </mi> <mo> - </mo> <mi> l </mi> </mrow> <mo> ❘ </mo> </mrow> </mrow> <mo> ⩵ </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn> 0 </mn> </mtd> <mtd> <mi> else </mi> </mtd> </mtr> </mtable> <mo mathcolor='#FFFFFF'> } </mo> </mrow> <mo> ) </mo> </mrow> <mtable> <mtr> <mtd> <mrow> <mn> 1 </mn> <mo> ≤ </mo> <mi> k </mi> <mo> ≤ </mo> <mi> n </mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 1 </mn> <mo> ≤ </mo> <mi> l </mi> <mo> ≤ </mo> <mi> n </mi> </mrow> </mtd> </mtr> </mtable> </msub> <mo> ❘ </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[LeftBracketingBar]", SubscriptBox[RowBox[List["(", StyleBox[RowBox[List["{", GridBox[List[List["1", RowBox[List[RowBox[List["if", " ", "k"]], "\[Equal]", "l"]]], List["\[ImaginaryI]", RowBox[List[RowBox[List["if", " ", RowBox[List["\[LeftBracketingBar]", RowBox[List["k", "-", "l"]], "\[RightBracketingBar]"]]]], "\[Equal]", "1"]]], List["0", "else"]]], StyleBox["}", Rule[FontColor, GrayLevel[1]]]]], Rule[SpanMaxSize, DirectedInfinity[1]]], ")"]], GridBox[List[List[RowBox[List["1", "\[LessEqual]", "k", "\[LessEqual]", "n"]]], List[RowBox[List["1", "\[LessEqual]", "l", "\[LessEqual]", "n"]]]]]], "\[RightBracketingBar]"]], List[Det]] </annotation> </semantics> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Fibonacci", "[", "n_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Det", "[", RowBox[List["Table", "[", RowBox[List[RowBox[List["Which", "[", RowBox[List[RowBox[List["k", "\[Equal]", "l"]], ",", "1", ",", RowBox[List[RowBox[List["Abs", "[", RowBox[List["k", "-", "l"]], "]"]], "\[Equal]", "1"]], ",", "\[ImaginaryI]", ",", "True", ",", "0"]], "]"]], ",", RowBox[List["{", RowBox[List["k", ",", "n"]], "}"]], ",", RowBox[List["{", RowBox[List["l", ",", "n"]], "}"]]]], "]"]], "]"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
