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 HarmonicNumber

 http://functions.wolfram.com/06.16.23.0004.01

 Input Form

 Sum[HarmonicNumber[k]^2/(k 2^k), {k, 1, Infinity}] == (7 Zeta[3])/8

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[SuperscriptBox[RowBox[List["HarmonicNumber", "[", "k", "]"]], "2"], RowBox[List["k", " ", SuperscriptBox["2", "k"]]]]]], "\[Equal]", FractionBox[RowBox[List["7", " ", RowBox[List["Zeta", "[", "3", "]"]]]], "8"]]]]]

 MathML Form

 k = 1 H HarmonicNumber k 2 k 2 k 7 ζ ( 3 ) TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e\$, Zeta[BoxForm`e\$]]]] 8 k 1 HarmonicNumber k 2 k 2 k -1 7 Zeta 3 8 -1 [/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_", "]"]], "2"], RowBox[List["k_", " ", SuperscriptBox["2", "k_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["7", " ", RowBox[List["Zeta", "[", "3", "]"]]]], "8"]]]]]

 Contributed by

 G.Huvent (2006)

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

 2007-05-02