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variants of this functions
EllipticPi






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticPi[n,z,m] > General characteristics > Branch points > With respect to z





http://functions.wolfram.com/08.06.04.0009.01









  


  










Input Form





BranchPoints[EllipticPi[n, z, m], z] == {SequenceList[ArcSin[1/Sqrt[m]] + Pi k, Element[k, Integers]], SequenceList[-ArcSin[1/Sqrt[m]] + Pi k, Element[k, Integers]], SequenceList[ArcSin[1/Sqrt[n]] + Pi k, Element[k, Integers]], SequenceList[-ArcSin[1/Sqrt[n]] + Pi k, Element[k, Integers]], SequenceList[Pi/2 + Pi k, Element[k, Integers] && !IntervalMemberQ[Interval[{0, 1}], m]], ComplexInfinity}










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BranchPoints", "[", RowBox[List[RowBox[List["EllipticPi", "[", RowBox[List["n_", ",", "z_", ",", "m_"]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List[RowBox[List["SequenceList", "[", RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", FractionBox["1", SqrtBox["m"]], "]"]], "+", RowBox[List["\[Pi]", " ", "k"]]]], ",", RowBox[List["k", "\[Element]", "Integers"]]]], "]"]], ",", RowBox[List["SequenceList", "[", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["ArcSin", "[", FractionBox["1", SqrtBox["m"]], "]"]]]], "+", RowBox[List["\[Pi]", " ", "k"]]]], ",", RowBox[List["k", "\[Element]", "Integers"]]]], "]"]], ",", RowBox[List["SequenceList", "[", RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", FractionBox["1", SqrtBox["n"]], "]"]], "+", RowBox[List["\[Pi]", " ", "k"]]]], ",", RowBox[List["k", "\[Element]", "Integers"]]]], "]"]], ",", RowBox[List["SequenceList", "[", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["ArcSin", "[", FractionBox["1", SqrtBox["n"]], "]"]]]], "+", RowBox[List["\[Pi]", " ", "k"]]]], ",", RowBox[List["k", "\[Element]", "Integers"]]]], "]"]], ",", RowBox[List["SequenceList", "[", RowBox[List[RowBox[List[FractionBox["\[Pi]", "2"], "+", RowBox[List["\[Pi]", " ", "k"]]]], ",", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["0", ",", "1"]], "}"]], "]"]], ",", "m"]], "]"]]]]]]]], "]"]], ",", "ComplexInfinity"]], "}"]]]]]]










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





2001-10-29





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