#### 7.69 Bug in hypergeom in Maple V.4 (23.9.96)

##### 7.69.1 Tony Blackett

Beware of a bug in Maple V R4 hypergeom function. The following examples illustrate the problem:

> readlib(hypergeom):
> hypergeom([2],[6],2*I*x);

2          3
I (1 + 3/2 I x - x  - 1/3 I x  - exp(2 I x) (1 - 1/2 I x))
-15 ----------------------------------------------------------
5
x



This ﬁrst computation causes no problems, but when k is used in place of x, we get a serious error:

> hypergeom([2],[6],2*I*k);
Error, (in sum) 0^0 is undefined
executing statement: convert([\$(e,x)],+)
locals defined as: r = r, sums = sums, k = k, naming = naming, unnaming =
unnaming, a = 0, ans = ans, b = 4, dab = 4, dxx = FAIL, i = i, tp = tp, xx =
k, np = np, oe = oe, ii = ii, mm = mm, rootslist = rootslist, dummy = dummy,
has_diffs = false, tmp = tmp, variable = variable
sum called with arguments:
pochhammer(-3,k)*(2*(-1)^(1/2)*k)^k/k!/pochhammer(-4,k), k = 0 .. 3



The hypergeom function uses k as a summation index, however, this variable has not been declared as a local variable. Consequently, the index variable k is assumed to be global and gets confused with the formal parameter variable that evaluates to 2*(-1)^(1/2)*k.

This one should be of interest to Technical Support and the Maple developers to ﬁx.

The bug is removed with Maple V Release 5. (U. Klein)