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 HarmonicNumber

 http://functions.wolfram.com/06.16.17.0005.01

 Input Form

 HarmonicNumber[z] == HarmonicNumber[z - n] + Sum[1/(z - k), {k, 0, n - 1}] /; Element[n, Integers] && n >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HarmonicNumber", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["HarmonicNumber", "[", RowBox[List["z", "-", "n"]], "]"]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["n", "-", "1"]]], FractionBox["1", RowBox[List["z", "-", "k"]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 H HarmonicNumber z H HarmonicNumber z - n + k = 0 n - 1 1 z - k /; n Condition HarmonicNumber z HarmonicNumber z -1 n k 0 n -1 1 z -1 k -1 n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HarmonicNumber", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["HarmonicNumber", "[", RowBox[List["z", "-", "n"]], "]"]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["n", "-", "1"]]], FractionBox["1", RowBox[List["z", "-", "k"]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2001-10-29