Transcendental Meromorphic Functions Whose First Order Derivatives Have Finitely Many Zeros
نویسندگان
چکیده
منابع مشابه
Non-real Zeros of Derivatives of Real Meromorphic Functions
The main result of the paper determines all real meromorphic functions f of finite order in the plane such that f ′ has finitely many zeros while f and f(k), for some k ≥ 2, have finitely many non-real zeros. MSC 2000: 30D20, 30D35.
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Let f be a function transcendental and meromorphic in the plane, and define g(z) by g(z) = ∆f(z) = f(z+1)− f(z). A number of results are proved concerning the existence of zeros of g(z) or g(z)/f(z), in terms of the growth and the poles of f . The results may be viewed as discrete analogues of existing theorems on the zeros of f ′ and f ′/f . MSC 2000: 30D35.
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ژورنال
عنوان ژورنال: Advances in Pure Mathematics
سال: 2019
ISSN: 2160-0368,2160-0384
DOI: 10.4236/apm.2019.911045