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[bug #58067] Missing asymptotic behavior of the airy Ai function

From: Britton Kerin
Subject: [bug #58067] Missing asymptotic behavior of the airy Ai function
Date: Sat, 28 Mar 2020 19:11:50 -0400 (EDT)
User-agent: Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/71.0.3578.98 Safari/537.36

Follow-up Comment #1, bug #58067 (project gsl):

[comment #0 original submission:]
> Using version 2.6 of GSL from ftp://ftp.gnu.org/gnu/gsl/gsl-2.6.tar.gz
> OS is Ubuntu 18.04.2 LTS
> Hardware is a Dell workstation with a 3.60 GHz Intel i7-4790 and 32 GB
> of RAM
> Compiler is gcc 7.4.0 with the -w option
> As the airy Ai function approaches positive infinity, its output goes to
> zero. The mathematical libraries mpmath, scipy, and jmat all represent
> this behavior, returning zero for large arguments (somewhere just
> past 100). On the other hand, GSL invokes the error handler with an
> underflow error, even though the proper behavior (theoretically) seems
> straightforward to represent

I don't know anything about that function in detail other than that it does
indeed appear to approach zero as you say.  But it isn't exactly zero, and
therefore it seems to me that the GSL behavior is correct.  If I intended to
approximate the value past some point I would expect to have to do that at the
level of the caller of this routine.



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