How do I justify this QDA expression for $a_k, ~b_{kj} $and $c_{jkl}$? I need to solve the equation of
$$\log\left(\frac{\operatorname{Pr}(Y=k|X=x)}{\operatorname{Pr}(Y=K|X=x)}\right)$$
$$=\log\left(\frac{\pi_k \exp\left((x-\mu_k)^T|\Sigma|^{-1}(x-\mu_k)\right)}
{\pi_K \exp\left((x-\mu_K)^T|\Sigma|^{-1}(x-\mu_K)\right)}\right)$$
to find the following constants $a_k$, $b_{kj}$ and $c_{kjl}$--

using the assumptions of quadratic discriminant analysis.

I think I got it, I was supposed to multiply and divide the original expression terms from LDA by $(n-K)/(n_k-1)$ and $(n-K)/(n_K-1)$ respectively. Please let me know if this is correct:

