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 PolyGamma

 http://functions.wolfram.com/06.14.23.0001.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], RowBox[List["PolyGamma", "[", "k", "]"]]]], "\[Equal]", RowBox[List["n", RowBox[List["(", RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List["n", "+", "1"]], "]"]], "-", "1"]], ")"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]]]]]]]]

 MathML Form

 k = 1 n ψ TagBox["\[Psi]", PolyGamma] ( k ) n ( ψ TagBox["\[Psi]", PolyGamma] ( n + 1 ) - 1 ) /; n + Condition k 1 n PolyGamma k n PolyGamma n 1 -1 n SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "n_"], RowBox[List["PolyGamma", "[", "k_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["n", " ", RowBox[List["(", RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List["n", "+", "1"]], "]"]], "-", "1"]], ")"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]

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

 2001-10-29