I'm looking through the proof of theorem 3.2 in this paper and struggling to understand why what applies to the polynomial P also applies to the coefficient of t^k.
http://www.ams.org/journals/proc/1977-065-02/S0002-9939-1977-0448394-2/S0002-9939-1977-0448394-2.pdf
If anyone has any helpful information it would be greatly appreciated.
Answered own question, it's all to do with the fact that the polynomial shrinks to 0 regardless of t for y close to x and s close to 0. Were at this point looking to equate a polynomial (f(t)=a_n*t^n+...+a_1*t+a_0) to the zero function. f(t) can only be equal to the zero function for all t if all the coefficients are 0.