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 HarmonicNumber

 http://functions.wolfram.com/06.16.23.0003.01

 Input Form

 Sum[HarmonicNumber[k]/(k^2 2^k), {k, 1, Infinity}] == Zeta[3] - (1/12) Pi^2 Log[2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["HarmonicNumber", "[", "k", "]"]], RowBox[List[SuperscriptBox["k", "2"], " ", SuperscriptBox["2", "k"]]]]]], "\[Equal]", RowBox[List[RowBox[List["Zeta", "[", "3", "]"]], "-", RowBox[List[FractionBox["1", "12"], " ", SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["Log", "[", "2", "]"]]]]]]]]]]

 MathML Form

 k = 1 H HarmonicNumber k k 2 2 k ζ ( 3 ) TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e\$, Zeta[BoxForm`e\$]]]] - 1 12 π 2 log ( 2 ) k 1 HarmonicNumber k k 2 2 k -1 Zeta 3 -1 1 12 2 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["HarmonicNumber", "[", "k_", "]"]], RowBox[List[SuperscriptBox["k_", "2"], " ", SuperscriptBox["2", "k_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Zeta", "[", "3", "]"]], "-", RowBox[List[FractionBox["1", "12"], " ", SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["Log", "[", "2", "]"]]]]]]]]]]

 Contributed by

 G.Huvent (2006)

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

 2007-05-02