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; }

 Cyclotomic

 http://functions.wolfram.com/05.11.20.0001.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["Cyclotomic", "[", RowBox[List["p", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], RowBox[List["p", "-", "1"]]], RowBox[List["k", " ", SuperscriptBox["z", RowBox[List["k", "-", "1"]]]]]]]]], "/;", " ", RowBox[List["p", "\[Element]", "Primes"]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["Cyclotomic", "[", RowBox[List["p_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], RowBox[List["p", "-", "1"]]], RowBox[List["k", " ", SuperscriptBox["z", RowBox[List["k", "-", "1"]]]]]]], "/;", RowBox[List["p", "\[Element]", "Primes"]]]]]]]]

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

 2001-10-29