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

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)