Handling branch cuts for hypergeometric functions

>>>>> "Wolfgang" == Wolfgang Jenkner  writes:

    Wolfgang> Raymond Toy  writes:
    >> These kinds of things always reminds of an example given in Kahan's
    >> paper Much Ado about Nothing's Sign.  He has an example two fairly
    >> complicated functions and asks if they're equal.  If you plug some
    >> random values, they are equal.  I think that if you do some naive
    >> manipulations, you'll prove that they are equal.  In fact, they are
    >> equal, except for in a small oval region of the plane, which you'd
    >> probably not find by random testing.  The difference arises because of
    >> the branch cuts of the functions involved.

    Wolfgang> But the `typical values' select only the premises of an implication,
    Wolfgang> say

    Wolfgang>    f=g => some result

    Wolfgang> It's still up to the user to work out if f=g is satisfied or not.

    Wolfgang> At least this is how I understand Albert Reiner's proposal in this
    Wolfgang> thread.

I was just wondering how useful it would be in more complicated
situations.   The example I gave was a great example but I think it
illustrates the pitfall of using "typical" values to decide
something.   But perhaps for the kinds of questions maxima asks, it is
ok.  I certainly haven't come up with a counterexample where this
would not work.

Ray