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Re: Bad Precision output for SphericaBesselY and BesselY

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123105] Re: Bad Precision output for SphericaBesselY and BesselY
  • From: Peter Pein <petsie at dordos.net>
  • Date: Wed, 23 Nov 2011 07:08:05 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <jafud8$rrr$1@smc.vnet.net>

Am 22.11.2011 11:43, schrieb Antonio Alvaro Ranha Neves:
> 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
>
>

Hi Antonio,

  to get an idea which input precision is needed to get an output 
precision of 90:

In[1]:= 
FindRoot[Precision[BesselY[301/2,SetPrecision[120.3,p]]]==90,{p,90},Evaluated->False]
Out[1]= {p->122.729}

the same for Accuracy gives {p -> 127.776}


hth,
Peter



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