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/06.17.11.0001.01

 Input Form

 HarmonicNumber[n, r] == SeriesTerm[PolyLog[r, t]/(1 - t), {t, 0, n}] /; Element[n, Integers] && n >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HarmonicNumber", "[", RowBox[List["n", ",", "r"]], "]"]], "\[Equal]", RowBox[List["SeriesTerm", "[", RowBox[List[FractionBox[RowBox[List["PolyLog", "[", RowBox[List["r", ",", "t"]], "]"]], RowBox[List["1", "-", "t"]]], ",", RowBox[List["{", RowBox[List["t", ",", "0", ",", "n"]], "}"]]]], "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 H HarmonicNumber n ( r ) - ( [ t n ] Li PolyLog r ( t ) 1 - t ) /; n TagBox["\[DoubleStruckCapitalN]", Function[Integers]] H HarmonicNumber n ( r ) - ( [ t n ] Li PolyLog r ( t ) 1 - t ) /; n TagBox["\[DoubleStruckCapitalN]", Function[Integers]] [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HarmonicNumber", "[", RowBox[List["n_", ",", "r_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["SeriesTerm", "[", RowBox[List[FractionBox[RowBox[List["PolyLog", "[", RowBox[List["r", ",", "t"]], "]"]], RowBox[List["1", "-", "t"]]], ",", RowBox[List["{", RowBox[List["t", ",", "0", ",", "n"]], "}"]]]], "]"]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2001-10-29