// degree 1 to degree k-1 coefficients
for (int i = 1; i < k; ++i) {
final BigFraction ckPrev = ck;
ck = coefficients.get(startK + i);
ckm1 = coefficients.get(startKm1 + i);
coefficients.add(ck.multiply(ai[0]).add(ckPrev.multiply(ai[1])).subtract(ckm1.multiply(ai[2])));
}
// degree k coefficient
final BigFraction ckPrev = ck;
ck = coefficients.get(startK + k);