I have a standard mathematical problem that I was wondering how to solve efficiently by mathematica. Here is the problem.
I have two power series expansions of a function F[x,y] = sum1 = sum2
A1 = (a/4)^2 (x^2 + y^2 + z^2);
A2 = (a/4)^3 x y z;
sum1 = Sum[A1^i * A2^j * P[i, j], {i, 0, 6}, {j, 0, 6}] /. {z -> -x - y}
sum2 = Sum[(a/4)^(i + j) (x^i y^j)/(i! j!) Q[i, j], {i, 0, 6}, {j, 0, 6}]
Basically I want to express one type of coefficients P[i,j]
in terms of Q[i,j]
.
P[i,j]
orQ[i,j]
are zero? $\endgroup$2 i + 3 j = n
wheren
is a natural number. $\endgroup$