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 EllipticF

 http://functions.wolfram.com/08.05.04.0003.01

 Input Form

 EllipticF[z + k Pi, m] == EllipticF[z, m] + 2 k EllipticK[m] /; Element[k, Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["z", "+", RowBox[List["k", " ", "\[Pi]"]]]], ",", "m"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["EllipticF", "[", RowBox[List["z", ",", "m"]], "]"]], "+", RowBox[List["2", " ", "k", " ", RowBox[List["EllipticK", "[", "m", "]"]]]]]]]], "/;", RowBox[List["k", "\[Element]", "Integers"]]]]]]

 MathML Form

 F ( z + π k m ) F ( z m ) + 2 k K ( m ) /; k TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition EllipticF z k m EllipticF z m 2 k EllipticK m k [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["z_", "+", RowBox[List["k", " ", "\[Pi]"]]]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["EllipticF", "[", RowBox[List["z", ",", "m"]], "]"]], "+", RowBox[List["2", " ", "k", " ", RowBox[List["EllipticK", "[", "m", "]"]]]]]], "/;", RowBox[List["k", "\[Element]", "Integers"]]]]]]]]

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

 2001-10-29