Abstract
In this paper, we prove the following Theorem Let f ( z ) be a transcendental meromorphic function on C , all of whose zeros have multiplicity at least k + 1 ( k ⩾ 2 ) , except possibly finitely many, and all of whose poles are multiple, except possibly finitely many, and let the function a ( z ) = P ( z ) exp ( Q ( z ) ) ≢ 0 , where P and Q are polynomials such that lim ¯ r → ∞ ( T ( r , a ) T ( r , f ) + T ( r , f ) T ( r , a ) ) = ∞ . Then the function f ( k ) ( z ) − a ( z ) has infinitely many zeros.
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