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)