This paper improves on the form of f +a(f(k))n,and extendf(k)to the differential polynomial L(f)about f.generalize the conditions to the differential polynomials,generalize the existing results,and by using the method of disproving,combine with the Zaclman-pang lemma,in this paper,two normal rules of form f +a(L(f))nare discussed and proved by constructing auxiliary functions.This paper consider the case of exceptional values and obtain that the family of meromorphic functions F is normal in the domain D when f+a(L(f))n≠b.This paper consider the case of shared values and obtain that if the zero of L(f)is not the b-value point of f(z)and for any two functionsfandgin F,f +a(L(f))nand g +a(L(g))nshare b,then F is normal on region D.
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