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 HarmonicNumber

 http://functions.wolfram.com/06.16.23.0005.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

 Contributed by

 G.Huvent (2006)

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

 2007-05-02