Taylor series.

can I write ?

i) T^n_a(f+g) = T^n_a(f) + T^n_a(g) ;

ii) T^n_a(f*g) = T^n_a[T^n_a(f) * T^n_a(g)] ;

iii) T^n_a(f \circ g) = T^n_a[T^n_{g(a)}(f) \circ T^n_a (g)];

can I also this ?

iii) T^n_a(f(g)) = T^n_a[T^n_{g(a)}(f(T^n_a(g)))]    ;


where I can find a guide of this taylor property in pdf?

Thanks to All !