html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 HarmonicNumber

 http://functions.wolfram.com/06.16.23.0006.01

 Input Form

 Sum[(HarmonicNumber[2 k] HarmonicNumber[2 k + 1])/(2 k + 1)^2, {k, 1, Infinity}] == Pi^4/64

 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[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], "2"]]]], "\[Equal]", FractionBox[SuperscriptBox["\[Pi]", "4"], "64"]]]]]

 MathML Form

 k = 1 H HarmonicNumber 2 k H HarmonicNumber 2 k + 1 ( 2 k + 1 ) 2 π 4 64 k 1 HarmonicNumber 2 k HarmonicNumber 2 k 1 2 k 1 2 -1 4 64 -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[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k_"]], "+", "1"]], ")"]], "2"]]]], "]"]], "\[RuleDelayed]", FractionBox[SuperscriptBox["\[Pi]", "4"], "64"]]]]]

 Contributed by

 G.Huvent (2006)

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

 2007-05-02