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variants of this functions
EllipticPi






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/08.06.04.0019.01









  


  










Input Form





BranchCuts[EllipticPi[n, z, m], z] == {SequenceList[{Interval[{ArcCsc[Sqrt[m]] + Pi k, Pi/2 + Pi k}], I}, Element[k, Integers] && Element[m, Reals] && m > 1 && !IntervalMemberQ[Interval[{1, Infinity}], n]], SequenceList[{Interval[{ArcCsc[Sqrt[m]] + Pi k, ArcCsc[Sqrt[n]] + Pi k}], I}, Element[k, Integers] && Element[m, Reals] && Element[n, Reals] && 1 < n < m], SequenceList[ {Interval[{ArcCsc[Sqrt[n]] + Pi k, Pi/2 + Pi k}], I}, Element[k, Integers] && Element[m, Reals] && Element[n, Reals] && 1 < n < m], SequenceList[ {Interval[{Pi/2 + Pi k, -ArcCsc[Sqrt[m]] + Pi (k + 1)}], -I}, Element[k, Integers] && Element[m, Reals] && m > 1 && !IntervalMemberQ[Interval[{1, Infinity}], n]], SequenceList[{Interval[{Pi/2 + Pi k, -ArcCsc[Sqrt[n]] + Pi (k + 1)}], -I}, Element[k, Integers] && Element[m, Reals] && Element[n, Reals] && 1 < n < m], SequenceList[{Interval[{-ArcCsc[Sqrt[n]] + Pi (k + 1), -ArcCsc[Sqrt[m]] + Pi (k + 1)}], -I}, Element[k, Integers] && Element[m, Reals] && Element[n, Reals] && 1 < n < m], SequenceList[{Interval[{ArcCsc[Sqrt[n]] + Pi k, Pi/2 + Pi k}], I}, Element[k, Integers] && !IntervalMemberQ[Interval[{1, Infinity}], m] && Element[n, Reals] && n > 1], SequenceList[ {Interval[{ArcCsc[Sqrt[n]] + Pi k, ArcCsc[Sqrt[m]] + Pi k}], I}, Element[k, Integers] && Element[m, Reals] && Element[n, Reals] && 1 < m < n], SequenceList[ {Interval[{ArcCsc[Sqrt[m]] + Pi k, Pi/2 + Pi k}], I}, Element[k, Integers] && Element[m, Reals] && Element[n, Reals] && 1 < m < n], SequenceList[ {Interval[{Pi/2 + Pi k, -ArcCsc[Sqrt[n]] + Pi (k + 1)}], -I}, Element[k, Integers] && !IntervalMemberQ[Interval[{1, Infinity}], m] && Element[n, Reals] && n > 1], SequenceList[ {Interval[{Pi/2 + Pi k, -ArcCsc[Sqrt[m]] + Pi (k + 1)}], -I}, Element[k, Integers] && Element[m, Reals] && Element[n, Reals] && 1 < m < n], SequenceList[{Interval[{-ArcCsc[Sqrt[m]] + Pi (k + 1), -ArcCsc[Sqrt[n]] + Pi (k + 1)}], -I}, Element[k, Integers] && Element[m, Reals] && Element[n, Reals] && 1 < m < n], SequenceList[{Interval[{Pi/2 + 2 Pi k, Pi/2 + 2 Pi k + I Infinity}], 1}, Element[k, Integers]], SequenceList[ {Interval[{(3 Pi)/2 + 2 Pi k, (3 Pi)/2 + 2 Pi k + I Infinity}], -1}, Element[k, Integers]], SequenceList[ {Interval[{Pi/2 + 2 Pi k - I Infinity, Pi/2 + 2 Pi k}], 1}, Element[k, Integers]], SequenceList[ {Interval[{(3 Pi)/2 + 2 Pi k - I Infinity, (3 Pi)/2 + 2 Pi k}], -1}, Element[k, Integers]]}










Standard Form





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MathML Form







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Rule Form





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





2007-05-02





© 1998- Wolfram Research, Inc.