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 PrimePi

 http://functions.wolfram.com/13.04.02.0001.01

 Input Form

 PrimePi[x] == Sum[UnitStep[x - Prime[k]], {k, 1, Floor[x]}] /; Element[x, Reals] && x >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["PrimePi", "[", "x", "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], RowBox[List["Floor", "[", "x", "]"]]], RowBox[List["UnitStep", "[", RowBox[List["x", "-", RowBox[List["Prime", "[", "k", "]"]]]], "]"]]]]]], "/;", " ", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "\[And]", RowBox[List["x", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 π TagBox["\[Pi]", PrimePi] ( x ) k = 1 x θ UnitStep ( x - prime ( k ) ) /; x TagBox["\[DoubleStruckCapitalR]", Function[Reals]] x 0 Condition PrimePi x k 1 x UnitStep x -1 prime k x x 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PrimePi", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], RowBox[List["Floor", "[", "x", "]"]]], RowBox[List["UnitStep", "[", RowBox[List["x", "-", RowBox[List["Prime", "[", "k", "]"]]]], "]"]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["x", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2001-10-29