This establishes a

recursion relation between the higher-order coefficients, 0), and the lowest order ones, [f.sup.(0)] (0) and [f.sup.(1)](0), and thus the power series is written in terms of only these two coefficients.

We obtain the

recursion relation from (15) and (18) as follows:

and require selecting zero constant for the inverse operation of the difference operator (E - 1) in computing [a.sup.(m).sub.n](m [greater than or equal to] 1), then the

recursion relation (14) uniquely determines [a.sup.(m).sub.n], [b.sup.(m).sub.n], [c.sup.(m).sub.n] (m [greater than or equal to] 1).

This assumption allows us to use the following

recursion relationThe

recursion relation for [[theta].sub.j] and [[delta].sub.j] is

Using the definition, we immediately obtain that the Clifford-Gegenbauer polynomials on [R.sup.m] satisfy the following

recursion relationWe show how they can be described by n x n matrices with polynomial entries and use this description to derive a

recursion relation for the iterations of the CA.

The expected reproductive output starting at age i with mortality rate [[mu].sub.i] will be denoted by V[[mu].sub.i]j): V([[mu].sub.i]) satisfies the

recursion relationFirst, we show that the [[??].sub.n](q; [omega]) satisfy an analogue of the

recursion relation (1), namely, (34) below.

Also, the recursive accumulator [[PSI].sup.n.sub.D] for the Drude pole obeys the following

recursion relationThe

recursion relation (12) can be shown as follows.