ABSTRACT
Now, choose N to be the number of terms to evaluate. Define a series of constants yk by yN+1=yN+2=0, and, for k=N,
Starting with k=N, evaluate yN, yN-1, …, y0. Now rewrite equation (145) as
The last few equations, for y0, y1, …, are
Multiply equation (147) by b0; equation (148), by b1; equation (149), by b2; and so
forth. Then sum the left - and right-hand sides of these equations. Summing the lefthand side yields S=Sbk. Now consider the contribution that the coefficients that multiply y3 make to the sum of the right-hand sides, which is
Similarly, we see that all the terms cancel that multiply yk for every k>1. Therefore,
the only terms that remain in the sum are
