I have two functions $F_1(a,b,x)$ and $F_2(a,b,x)$ I expand these functions about the point $x=0$
Series[F1,{x,0,2}]
Series[F2,{x,0,2}]
the coefficients are depended on $a$ and $b$ variables. I want to create the system of equations where all coefficients are equal to zero.
$$F_1(a,b,x)=A_0(a,b)+A_1(a,b)x+A_2(a,b)x^2$$ $$F_2(a,b,x)=B_0(a,b)+B_1(a,b)x+B_2(a,b)x^2$$
so the system of the equations is
$A_0(a,b)=0, \ A_1(a,b)=0, \ A_2(a,b)=0, B_0(a,b)=0, \ B_1(a,b)=0, \ B_2(a,b)=0$
I know that CoefficientList[Series[F1,{x,0,2}],{x}]
returns coefficients of the expansion, but how can I use them to create equations? And how can I pass them to Solve[]
function?
Solve[Thread[coeffs == 0], (* stuff *)]
. Your system is currently overdetermined, however. $\endgroup$Thread[]
did to solve your problem, I would suggest writing an answer to your own question. $\endgroup$