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 Cyclotomic

 http://functions.wolfram.com/05.11.21.0001.01

 Input Form

 Integrate[Cyclotomic[p, z], z] == Sum[z^(k + 1)/(k + 1), {k, 0, p - 1}] /; Element[p, Primes]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Cyclotomic", "[", RowBox[List["p", ",", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["p", "-", "1"]]], FractionBox[SuperscriptBox["z", RowBox[List["k", "+", "1"]]], RowBox[List["k", "+", "1"]]]]]]], "/;", " ", RowBox[List["p", "\[Element]", "Primes"]]]]]]

 MathML Form

 C TagBox["C", Cyclotomic] p ( z ) z k = 0 p - 1 z k + 1 k + 1 /; p TagBox["\[DoubleStruckCapitalP]", Function[Primes]] Condition z Cyclotomic p z k 0 p -1 z k 1 k 1 -1 p [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["Cyclotomic", "[", RowBox[List["p_", ",", "z_"]], "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["p", "-", "1"]]], FractionBox[SuperscriptBox["z", RowBox[List["k", "+", "1"]]], RowBox[List["k", "+", "1"]]]]], "/;", RowBox[List["p", "\[Element]", "Primes"]]]]]]]]

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

 2001-10-29