The difficulty and cost of performing the symbolic integration and
differentiation operations indicated in (4) can be greatly reduced by
approximating as follows: first, expand , the
numerator of , into a sum of individual terms; next, write as ; next, expand
using the binomial theorem to 18 terms; next, multiply together the
resulting numerator and denominator expressions; finally, omit all
terms whose exponent of is greater than 18. The result is a
linear sum of terms of the form for modest-sized
integers p and q.