First derivative (\( f_0 = f(x_0) \), \( f_{-h}=f(x_0-h) \) and \( f_{+h}=f(x_0+h) \) $$ \frac{f_h-f_{-h}}{2h}=f'_0+\sum_{j=1}^{\infty}\frac{f_0^{(2j+1)}}{(2j+1)!}h^{2j}. $$ Second derivative $$ \frac{ f_h -2f_0 +f_{-h}}{h^2}=f_0''+2\sum_{j=1}^{\infty}\frac{f_0^{(2j+2)}}{(2j+2)!}h^{2j}. $$