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 HarmonicNumber

 http://functions.wolfram.com/06.16.23.0007.01

 Input Form

 Sum[(HarmonicNumber[2 k] HarmonicNumber[2 k - 1])/k^2, {k, 1, Infinity}] == (17 Pi^4)/240

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["HarmonicNumber", "[", RowBox[List["2", " ", "k"]], "]"]], " ", RowBox[List["HarmonicNumber", "[", RowBox[List[RowBox[List["2", " ", "k"]], "-", "1"]], "]"]]]], SuperscriptBox["k", "2"]]]], "\[Equal]", FractionBox[RowBox[List["17", " ", SuperscriptBox["\[Pi]", "4"]]], "240"]]]]]

 MathML Form

 k = 1 H HarmonicNumber 2 k H HarmonicNumber 2 k - 1 k 2 17 π 4 240 k 1 HarmonicNumber 2 k HarmonicNumber 2 k -1 k 2 -1 17 4 240 -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["HarmonicNumber", "[", RowBox[List["2", " ", "k_"]], "]"]], " ", RowBox[List["HarmonicNumber", "[", RowBox[List[RowBox[List["2", " ", "k_"]], "-", "1"]], "]"]]]], SuperscriptBox["k_", "2"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["17", " ", SuperscriptBox["\[Pi]", "4"]]], "240"]]]]]

 Contributed by

 G.Huvent (2006)

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

 2007-05-02