Setting either argument to zero in the expansion and comparing coefficients gives
$$
\boxed{F^r=0,\qquad A=B=1,\qquad
D^r{}_{st}=E^r{}_{st}=0}.
$$
Thus, through quadratic order,
$$
\varphi^r(x,y)=x^r+y^r+C^r{}_{st}x^sy^t+O(3).
$$


Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 302 / 2 / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-302/2/ii/solution