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Problem with LegendreQ


I seem to be getting incorrect numerical results for the LegendreQ[n,x]
function.  For example I get:



LegendreQ[-1/2,5]//N     =    1.00108 -1.17142 i


so that the imaginary part is not zero.  However, using the identity
(Abramowitz and Stegun 8.3.13):

LegendreQ[-1/2, x] = Sqrt[2/(x+1)] * EllipticK[Sqrt[2/(x+1)]]

The answer should be:

Sqrt[2/(5+1)]EllipticK[Sqrt[2/(5+1)]]//N

 1.11187


Michael Mandelberg


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