Re: MarcumQ function

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• Subject: [mg130698] Re: MarcumQ function
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Fri, 3 May 2013 03:52:29 -0400 (EDT)
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```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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