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 Fibonacci

 http://functions.wolfram.com/04.11.23.0004.01

 Input Form

 Sum[1/Fibonacci[2 k - 1], {k, 1, Infinity}] == (Sqrt[5]/4) EllipticTheta[2, 0, 2/(3 + Sqrt[5])]^2

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox["1", RowBox[List["Fibonacci", "[", RowBox[List[RowBox[List["2", "k"]], "-", "1"]], "]"]]]]], "\[Equal]", RowBox[List[FractionBox[SqrtBox["5"], "4"], SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "0", ",", FractionBox["2", RowBox[List["3", "+", SqrtBox["5"]]]]]], "]"]], "2"]]]]]]]

 MathML Form

 k = 1 1 F TagBox["F", Fibonacci] 2 k - 1 1 4 5 ϑ 2 ( 0 , 2 3 + 5 ) 2 k 1 1 Fibonacci 2 k -1 -1 1 4 5 1 2 EllipticTheta 2 0 2 3 5 1 2 -1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "\[Infinity]"], FractionBox["1", RowBox[List["Fibonacci", "[", RowBox[List[RowBox[List["2", " ", "k_"]], "-", "1"]], "]"]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "4"], " ", SqrtBox["5"], " ", SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "0", ",", FractionBox["2", RowBox[List["3", "+", SqrtBox["5"]]]]]], "]"]], "2"]]]]]]]

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

 2001-10-29