--- franktaw@netscape.net wrote:
Find a strictly increasing sequence of positive integers a(k) such that
(a(0) + a(1)*x + a(2)*x^2 + a(3)*x^3 + ...) * (a(0) - a(1)*x + a(2)*x^2 - a(3)*x^3 + ...) = 1.
Note: there are infinitely many solutions. One with a radius of convergence of 1 would be preferred. (No radius of convergence larger than 1 is possible with the given conditions.)
Franklin T. Adams-Watters
If the first series is the expansion of f(x), then f(x)*f(-x) = 1. So try (1+x)/(1-x). Its series does not have strictly increasing coefficients. Then square this function, and that works. Gene __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com