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[tex]A(T,M)=\sum^{\infty}_{j=0}L_j(T)M^j=L_0(T)+L_2(T)M^2+L_4(T)M^4+...[/tex]

Why [tex]A(T,M)[/tex] must be even function of [tex]M[/tex]?

Coefficients can be expanded about [tex]T=T_c[/tex]

[tex]L_j(T)=\sum^{\infty}_{k=0}l_{jk}(T-T_c)^k=l_{j0}+l_{j1}(T-T_c)+...[/tex]

How I could no that coefficients are analytic functions od [tex]T[/tex].