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WeierstrassHalfPeriods






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassHalfPeriods[{g2,g3}] > Integral representations > On the real axis > Of the direct function





http://functions.wolfram.com/09.18.07.0001.01









  


  










Input Form





WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}] == {Integrate[1/Sqrt[4 t^3 - Subscript[g, 2] t - Subscript[g, 3]], {t, Subscript[e, 1], Infinity}], I Integrate[1/Sqrt[4 t^3 - Subscript[g, 2] t - Subscript[g, 3]], {t, -Infinity, Subscript[e, 3]}]} /; Element[Subscript[g, 2], Reals] && Element[Subscript[g, 3], Reals] && Subscript[g, 2]^3 - 27 Subscript[g, 3]^2 > 0 && 4 t^3 - Subscript[g, 2] t - Subscript[g, 3] == 4 (t - Subscript[e, 1]) (t - Subscript[e, 2]) (t - Subscript[e, 3]) && Subscript[e, 1] > Subscript[e, 2] > Subscript[e, 3]










Standard Form





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MathML Form







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Rule Form





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2001-10-29





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