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 HarmonicNumber

 http://functions.wolfram.com/06.16.23.0013.01

 Input Form

 Sum[(HarmonicNumber[k]/k^3) Cos[(Pi k)/3], {k, 1, Infinity}] == (17 Pi^4)/4860

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List["HarmonicNumber", "[", "k", "]"]], SuperscriptBox["k", "3"]], RowBox[List["Cos", "[", FractionBox[RowBox[List["\[Pi]", " ", "k"]], "3"], "]"]]]]]], "\[Equal]", FractionBox[RowBox[List["17", SuperscriptBox["\[Pi]", "4"]]], "4860"]]]]]

 MathML Form

 k = 1 H HarmonicNumber k k 3 cos ( π k 3 ) 17 π 4 4860 k 1 HarmonicNumber k k 3 -1 k 3 -1 17 4 4860 -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", "[", "k_", "]"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["\[Pi]", " ", "k_"]], "3"], "]"]]]], SuperscriptBox["k_", "3"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["17", " ", SuperscriptBox["\[Pi]", "4"]]], "4860"]]]]]

 Contributed by

 G.Huvent (2006)

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

 2007-05-02