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; }

 PolyLog

 http://functions.wolfram.com/10.08.23.0004.01

 Input Form

 Sum[PolyLog[2 k + 1, 1]/2^(2 k + 1), {k, 1, Infinity}] == Log[2] - 1/2

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["PolyLog", "[", RowBox[List[RowBox[List[RowBox[List["2", "k"]], "+", "1"]], ",", "1"]], "]"]], SuperscriptBox["2", RowBox[List[RowBox[List["2", "k"]], "+", "1"]]]]]], "\[Equal]", RowBox[List[RowBox[List["Log", "[", "2", "]"]], "-", FractionBox["1", "2"]]]]]]]

 MathML Form

 k = 1 Li PolyLog 2 k + 1 ( 1 ) 2 2 k + 1 log ( 2 ) - 1 2 k 1 PolyLog 2 k 1 1 2 2 k 1 -1 2 -1 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["PolyLog", "[", RowBox[List[RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ",", "1"]], "]"]], SuperscriptBox["2", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Log", "[", "2", "]"]], "-", FractionBox["1", "2"]]]]]]]

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

 2001-10-29