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Re: MarcumQ function


It's a precision issue. Specify a working precision rather than using
machine precision; however, it slows down the computations.


Plot[{
  MarcumQ[100, 10, x],
  1 - MarcumQ[100, 10, 0, x]},
 {x, 0, 30},
 WorkingPrecision -> 20]


Plot[{
  MarcumQ[51, 10, x],
  1 - MarcumQ[51, 10, 0, x]},
 {x, 0, 30},
 WorkingPrecision -> 20]



Bob Hanlon




On Wed, May 1, 2013 at 9:43 PM, Donagh Horgan <donagh.horgan at gmail.com>wrote:

> Hello,
>
> I recently upgraded to Mathematica 9, and I've noticed a problem with the
> MarcumQ function. The following command should illustrate it:
>
> Plot[{MarcumQ[100, 10, x], 1 - MarcumQ[100, 10, 0, x]}, {x, 0, 30}]
>
> While the two functions are mathematically equivalent, the second
> incorrectly evaluates to zero between (approximately) x = 14 and x = 17.
>
> The problem only seems to occur when the first parameter is large. For
> example, the command
>
> Plot[{MarcumQ[50, 10, x], 1 - MarcumQ[50, 10, 0, x]}, {x, 0, 30}]
>
> evaluates correctly, while the command
>
> Plot[{MarcumQ[51, 10, x], 1 - MarcumQ[51, 10, 0, x]}, {x, 0, 30}]
>
> does not.
>
> I've tried wrapping the functions with the N command, e.g. N[f, 100], but
> the same problem occurs. I've also tried increasing $MaxExtraPrecision and
> $WorkingPrecision using Block, but with no luck.
>
> I've been testing my old code since I upgraded from Mathematica 8 a few
> days ago, so the error appears (to me, at least) to be new.
>
> All suggestions greatly appreciated!
>
> Best regards,
> Donagh Horgan
>
>




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