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 HarmonicNumber

 http://functions.wolfram.com/06.16.16.0006.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29