Centered form

Let $P=sum_{i=0}^{i=n} a_i x^i$ which may also be written as $sum_{i=0}^{i=n} b_i(x-a)^i$ where $a$ is some fixed or interval value. The coefficient $b_i$ may be calculated with the procedure

 
int Derive_Polynomial_Expansion(int n,INTERVAL_VECTOR &Coeff,INTERVAL &a,INTERVAL_VECTOR &B)

which returns 1 if the $b_i$ have been successfully calculated (0 otherwise). The coefficients of $P$ are Coeff and the $b_i$ are stored in B.