so that the two-term
recurrence relation (51) can be rewritten as ([c.sub.0] = 1)
Proof: Upon extending [u.sub.n] to the negative integers using the
recurrence relation [u.sub.-4] = [3u.sub.n-2] - [u.sub.n], we note that [u.sub.n] = -[u.sub.-n-2].
For each fixed m, these two generating functions share the same denominator, hence the same
recurrence relation. We used Pascal programs and Mathematica 6 to carry out the computation.
A
recurrence relation for marginal moment generating function for lgos from df (1.5) can be obtained in the following theorem.
Then method of lines, semidiscritization approach, is used to transform the model partial differential equation into a system of first-order linear ordinary differential equations whose solution satisfies a
recurrence relation involving matrix exponential function.
Moreover, combining the annihilation equation and the recursion formula (6) we obtain the following
recurrence relation.
Firstly find the
recurrence relation for coefficients and construct with it a program using the calculator to automatically generate coefficients of the series.
It is known that the
recurrence relation for incomplete gamma functions {[Lambda] (a + n, x)}, 0 [is less than or equal to] a [is less than] 1, n = 0, 1,2, ..., when x is positive, is unstable--more so the larger x.
Then the
recurrence relation (2.25) can be expressed as
After studying it carefully, it is found that the solutions cannot be given exactly due to the complicated three-term
recurrence relation. The method used by him is nothing but the Bethe ansatz method as summarized in [13].
Then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the characteristic polynomial which determines the
recurrence relation that [h.sub.m](n) satisfies.