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   http://functions.wolfram.com/04.11.26.0020.01
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    Fibonacci[2 n]^2 == (4/5) n^2 HypergeometricPFQ[{1 - 2 n, 1, 2 n + 1}, 
    {3/2, 2}, -(1/4)] /; Element[n, Integers] 
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   Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Fibonacci", "[", RowBox[List["2", "n"]], "]"]], "2"], "\[Equal]", RowBox[List[FractionBox["4", "5"], SuperscriptBox["n", "2"], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", RowBox[List["2", "n"]]]], ",", "1", ",", RowBox[List[RowBox[List["2", "n"]], "+", "1"]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", "2"]], "}"]], ",", RowBox[List["-", FractionBox["1", "4"]]]]], "]"]]]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]] 
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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>  <mrow>  <msubsup>  <semantics>  <mi> F </mi>  <annotation encoding='Mathematica'> TagBox["F", Fibonacci] </annotation>  </semantics>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> n </mi>  </mrow>  <mn> 2 </mn>  </msubsup>  <mo> ⩵ </mo>  <mrow>  <mfrac>  <mn> 4 </mn>  <mn> 5 </mn>  </mfrac>  <mo> ⁢ </mo>  <msup>  <mi> n </mi>  <mn> 2 </mn>  </msup>  <mo> ⁢ </mo>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 3 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> n </mi>  </mrow>  </mrow>  <mo> , </mo>  <mn> 1 </mn>  <mo> , </mo>  <mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> n </mi>  </mrow>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  </mrow>  <mo> ; </mo>  <mrow>  <mfrac>  <mn> 3 </mn>  <mn> 2 </mn>  </mfrac>  <mo> , </mo>  <mn> 2 </mn>  </mrow>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 1 </mn>  <mn> 4 </mn>  </mfrac>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["1", "-", RowBox[List["2", " ", "n"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["2", " ", "n"]], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["2", HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", "4"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation>  </semantics>  </mrow>  </mrow>  <mo> /; </mo>  <mrow>  <mi> n </mi>  <mo> ∈ </mo>  <semantics>  <mi> ℤ </mi>  <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation>  </semantics>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <ci> Condition </ci>  <apply>  <eq />  <apply>  <power />  <apply>  <ci> Fibonacci </ci>  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> n </ci>  </apply>  </apply>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <times />  <cn type='rational'> 4 <sep /> 5 </cn>  <apply>  <power />  <ci> n </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> n </ci>  </apply>  </apply>  </apply>  <cn type='integer'> 1 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> n </ci>  </apply>  <cn type='integer'> 1 </cn>  </apply>  </list>  <list>  <cn type='rational'> 3 <sep /> 2 </cn>  <cn type='integer'> 2 </cn>  </list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 1 <sep /> 4 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <in />  <ci> n </ci>  <integers />  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
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  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["Fibonacci", "[", RowBox[List["2", " ", "n_"]], "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["4", "5"], " ", SuperscriptBox["n", "2"], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", RowBox[List["2", " ", "n"]]]], ",", "1", ",", RowBox[List[RowBox[List["2", " ", "n"]], "+", "1"]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", "2"]], "}"]], ",", RowBox[List["-", FractionBox["1", "4"]]]]], "]"]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]  |  
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   Date Added to functions.wolfram.com (modification date)
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