On 04/06/2026 02:30, Waldek Hebisch wrote:
...
But there is another possible trouble: evaluating input function
at upper or lower bound may also lead to division by 0. Input
may have pole at bound, in such case division by 0 is unavoidable.
But another case is when already input contains trouble similar to
the first case. That is rational part of input is supposed to
cancel with factorial or binomial part. AFAICS we need better
version of 'eval' to transform input (cancel zeros) first and
only evaluate after transformation.
Indeed,as you say, it's even worse. Your example gives
>> Error detected within library code:
factorial not defined for negative integers
which clearly shows that a summand is tried to be evaluated outside of
the domain of definition.
In the book "A=B" on p. 77, where Gosper's algorithm is summarized the
following (IMO) cryptic passage is a mystery to me.
---
Once we have zn , the sum that we are looking for is sn = zn − z0 . The
lower summation bound need not be 0; for example, it may happen that the
summand in (5.1.1) is undefined for certain integer values of k, and
then we will want to start the summation at some large enough value to
skip over all the singularities. If the lower summation bound is k0,
then everything goes through as before, except that now sn = zn − zk0 .
---
I guess we may assume that in finite summation the summands are well
defined over the segment? Well, I leave it to you to rethink the whole
matter :)
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