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Re: Bad Precision output for SphericaBesselY and BesselY

• To: mathgroup at smc.vnet.net
• Subject: [mg123083] Re: Bad Precision output for SphericaBesselY and BesselY
• From: "Oleksandr Rasputinov" <oleksandr_rasputinov at hmamail.com>
• Date: Wed, 23 Nov 2011 07:04:03 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jafud8$rrr$1@smc.vnet.net>

On Tue, 22 Nov 2011 10:43:52 -0000, Antonio Alvaro Ranha Neves  
<aneves at gmail.com> wrote:

> Dear users,
>
> Recently I'm working with precision calculations of spherical functions.  
> Example, let,
>
> n = 150
> x = SetPrecision[120.3, 100]
> BesselY[n + 1/2, x] // Precision
> BesselJ[n+ 1/2, x] // Precision
>
>
> Yields 67.2708 and 96.9297 respectively. The two questions are:
> 1) Why does BesselY results in a worse than BesselJ?
> 2) How to redefine, BesselY to automatically output a result with a  
> desired pecision?
>
> Note: Simply using N[expr,90], does not yield a result of expr with 90  
> precision but maintains the same 67.2708.
>
> Thanks,
> Antonio
>
>

Both functions lose precision, and BesselY loses a lot. Why this would be  
I don't know off-hand as I'm not sure what method these functions use to  
calculate their outputs. However, the essential problem is that there  
isn't enough precision in your input. If you try

x = SetPrecision[120.3, Infinity]

or better

x = Rationalize[120.3]

then N is able to give you an output with the full 90 digits of precision  
in both cases.