

Ask HN: Rent a mathematician / numerical analyst? - jey

Is there some place where I can pay to have math problems solved?<p>Specifically I'm looking for a fast accurate floating point implementation of log(I_n(x)) where I_n(x) is the modified Bessel function of the first kind. There are nice implementations of I_n(x) but taking the logarithm after the fact is awful for accuracy. Doing this right probably involves expressing it in terms of Chebyshev polynomials or some other weird functional analysis that I don't really feel like learning.
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yummyfajitas
This sounds dangerously close to a homework problem, so my response will be in
the form of homework hints.

I'll assume you want I(n,x) for integer n. For small-to-moderate x, write
I(n,x) as a power series, peel off the leading order x^n term, then take the
log of the right side and use properties of logs to get n log(x)+log(c+o(x)).
The result should be just as accurate as your logarithm function.

For large x, use the asymptotic expansion of I(n,x) and again use properties
of logarithms.

To figure out where the boundary of "small-to-moderate" and "large" lies, see
Abramowitz&Stegun.

If you aren't a student, please accept my apologies. Feel free to email me
(email in profile), I'll give you more info if you reciprocate by telling me
where you came across this problem. If it's not a homework problem, it looks
interesting.

~~~
jey
Not a student, but I do appreciate the hints! In my case I need it to work for
positive real values of x and values of n=y/2 where y is a positive integer.

As for why this comes up: I'm working on a statistical estimation problem and
this is part of the normalization term in my log-posterior.

Again, thanks for the hints. I'll try my hand at solving it.

