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Re: besseli: Am I missing something?


From: Robert T. Short
Subject: Re: besseli: Am I missing something?
Date: Thu, 12 Jan 2012 06:16:17 -0800
User-agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.9.1.4) Gecko/20091017 SeaMonkey/2.0

Robert T. Short wrote:
Before I file a bug report, maybe I should check that I am not all wet.

If I recall my Bessel function theory,

besseli(n,x) = besseli(-n,x)

if n is an integer.

In octave 3.4.2 I get

octave:3> besseli(1,1),besseli(-1,1)
ans =  0.565159103992485
ans =  0.565159103992485

Looks good for n=1, but for n=10

octave:4> besseli(10,1),besseli(-10,1)
ans =  2.75294803983687e-10
ans = -1.40610343427994e-07

Not so good!

And for n=100

octave:5> besseli(100,1),besseli(-100,1)
ans =  8.47367400813812e-189
ans =  7.38028373423800e+170

BTW, the numbers for positive n agree to about 9 or 10 decimal places with my tables. Also, BTW, the relationships for besselj seem to work fine.

Anybody?

Bob


Well, I will file the report. I will also make some tests for this and other cases.

I have already determined that the octave implementation is only good to maybe 9 places in other situations. Since Amos used asymptotic expansions in some cases, I can't imagine how we would get more, but I am not a numerical analysist. Since I am messing with this stuff, I will dig deeper and report back. Thanks for the comments and pointers.

Bob



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