$\langle k^n \rangle = \sum_a F(a)\langle k^n|a \rangle=\sum_a F(a) \sum_k k^n g(k|a) =\sum_a F(a) \sum_m\genfrac{\{}{\}}{0pt}{}{n}{m}\lambda^m =\sum_a F(a)\sum_m\genfrac{\{}{\}}{0pt}{}{n}{m}[T(a+\langle a\rangle)]^m =\sum_m\genfrac{\{}{\}}{0pt}{}{n}{m}T^m\sum_a F(a)(a+\langle a\rangle)^m =\sum_m\genfrac{\{}{\}}{0pt}{}{n}{m}T^m\kappa_m$

arxiv.org/abs/cond-mat/9606196 stated that if u in the right hand of M=F(u) depend on left hand of the equation. The equation is self-consistency. So, Does it mean if something is self-consistency, there should be a function like M=F(u)?

It seems say that Mean_field_theory is self-consistent. But what is self-consistent.