[Maxima] Problems with hypergeo21(a,b,c,x,-n)

Kris Katterjohn katterjohn at gmail.com
Sat Oct 27 16:52:53 CDT 2012

Hey again,

On 10/03/2012 09:01 PM, Kris Katterjohn wrote:
> I've found a bug in assoc_legendre_p(): the results seem to always be zero
> when a negative degree is given.

The hypergeo21() function in orthopoly.lisp, which a lot (all?) of the
orthopoly functions eventually call, doesn't seem to handle negative n index
values correctly either.  One issue is that it tries to sum from 0 to n, and
so it seems to always gives 0 for negative integer n limits.  This means that
it seems to affect a lot more than I initially thought.

I'm currently pretty busy, so I cannot look into this further at the moment.
I can try to look into this later when I have more time if nobody has any
ideas.  I just wanted to get this out there.

A related issue is that it seems the same sum can be done from 0 to some
non-integer (possibly negative) value.  I'm not currently sure of the best way
to handle this either.

In regard to my patches: assoc_legendre_p() is becoming identically zero for a
different reason (a check for |m|>n for negative n, before anything else), but
legendre_p() is becoming identically zero because of hypergeo21().  Either
way, my patches give much nicer results for negative integer n degrees than
any result from hypergeo21().

Kris Katterjohn

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