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Re: Bad Precision output for SphericaBesselY and

• To: mathgroup at smc.vnet.net
• Subject: [mg123078] Re: Bad Precision output for SphericaBesselY and
• From: Oliver Ruebenkoenig <ruebenko at wolfram.com>
• Date: Tue, 22 Nov 2011 07:23:18 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201111221036.FAA28073@smc.vnet.net>

On Tue, 22 Nov 2011, Antonio Alvaro Ranha Neves 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
>
>
>

Antonio,

you could use exact arithmetic and only later derive the numeric 
quantities.

n = 150
x = 1203/10
BesselY[n + 1/2, x] // Precision
BesselJ[n + 1/2, x] // Precision

N[BesselY[n + 1/2, x], 100] // Precision
N[BesselJ[n + 1/2, x], 100] // Precision

gives a precision of 100. for both.

Oliver

• References:
  • Bad Precision output for SphericaBesselY and BesselY
    • From: Antonio Alvaro Ranha Neves <aneves@gmail.com>