Cancellations in power series of sine type

Juan Arias de Reyna

We present a method to study the behavior of a power series of type $$f(x):=\sum _{n=0}^{\infty }(-1{)}^n{c}_n\frac{x^{2n+1}}{(2n+1)!}$$ when $x\to \infty$. We apply our method to study t…