The function is based on a Chebyshev expansion for (1+u), and uses the property (1+x) = x(x).
If x = N +1+u where N is integral and 0 ≤ u < 1 then it follows that:
for N >0 (x) = (x - 1)(x - 2) . . . (x - N)(1 + u)
for N = 0 (x) = (1+u)
for N <0 (x) = (1+u)/x(x + 1)(x + 2) . . . (x - N - 1).
For more information please review the s14aac function in the NAG document