f1[u_,v_]:=(1+(1/4) (8 (u^2)-n (u^4)+8 (v^2)-2 n (u^2) (v^2)-n (v^4))+(1/96) (288 (u^4)-64 n (u^6)+3 (n^2) (u^8)+576 (u^2) (v^2)-192 n (u^4) (v^2)+12 (n^2) (u^6) (v^2)+288 (v^4)-192 n (u^2) (v^4)+18 (n^2) (u^4) (v^4)-64 n (v^6)+12 (n^2) (u^2) (v^6)+3 (n^2) (v^8)))Exp[-n (u^2+v^2)/2]

f2[u_,v_]:=(1+(1/4) (6 (u^2)-n (u^4)+6 (v^2)-n (v^4))+(1/(96 n))(-48 (u^2)+180 n (u^4)-52 (n^2) (u^6)+3 (n^3) (u^8)-48 (v^2)+264 n (u^2) (v^2)-36 (n^2) (u^4) (v^2)+180 n (v^4)-36 (n^2) (u^2) (v^4)+6 (n^3) (u^4) (v^4)-52 (n^2) (v^6)+3 (n^3) (v^8)))Exp[-n (u^2+v^2)/2]