Left tail of incomplete Gamma function:

            inf.      k
     a  -x   -       x
    x  e     >   ----------
             -     -
            k=0   | (a+k+1)

def _igam(a, x):
    """Left tail of incomplete Gamma function:

            inf.      k
     a  -x   -       x
    x  e     >   ----------
             -     -
            k=0   | (a+k+1)
    """
    # Compute  x**a * exp(-x) / Gamma(a)
    ax = math.exp(a * math.log(x) - x - math.lgamma(a))

    # Power series
    r = a
    c = 1.0
    ans = 1.0

    while True:
        r += 1.0
        c *= x/r
        ans += c
        if c / ans <= MACHEP:
            return ans * ax / a