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 DigitCount

 http://functions.wolfram.com/13.10.23.0006.01

 Input Form

 Sum[(DigitCount[k, 2, 1] (2 k + 1))/(k^2 (k + 1)^2), {k, 1, Infinity}] == Pi^2/9

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["DigitCount", "[", RowBox[List["k", ",", "2", ",", "1"]], "]"]], RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]]]], RowBox[List[SuperscriptBox["k", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], "2"]]]]]], "\[Equal]", FractionBox[SuperscriptBox["\[Pi]", "2"], "9"]]]]]

 MathML Form

 k = 1 2 k + 1 k 2 ( k + 1 ) 2 s 2 ( 1 ) ( k ) π 2 9 k 1 2 k 1 k 2 k 1 2 -1 Subscript s 2 1 k 2 9 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["DigitCount", "[", RowBox[List["k", ",", "2", ",", "1"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]]]], RowBox[List[SuperscriptBox["k", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], "2"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[SuperscriptBox["\[Pi]", "2"], "9"]]]]]

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

 2001-10-29