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- Title
UNIQUENESS OF SHIFT AND DERIVATIVES OF MEROMORPHIC FUNCTIONS.
- Authors
PRAMANIK, D. C.; SARKAR, A.
- Abstract
This paper addresses the uniqueness problem concerning the j-th derivative of a meromorphic function f(z) and the k-th derivative of its shift, f(z + c), where j, k are integers with 0 ≤ j < k. In this regard, our work surpasses the achievements of [2], as we have improved upon the existing results and provided a more refined understanding of this specific aspect. We give some illustrative examples to enhance the realism of the obtained outcomes. Denote by E(a, f) the set of all zeros of f-a, where each zero with multiplicity m is counted m times. In the paper proved, in particular, the following statement: Let f(z) be a non-constant meromorphic function of finite order, c be a non-zero finite complex number and j, k be integers such that 0 ≤ j < k. If f(j)(z) and f(k)(z + c) have the same a-points for a finite value a(̸= 0) and satisfy conditions...
- Subjects
MEROMORPHIC functions; UNIQUENESS (Mathematics); DERIVATIVES (Mathematics); MODULES (Algebra); INTEGERS; MULTIPLICITY (Mathematics)
- Publication
Matematychni Studii, 2024, Vol 61, Issue 2, p160
- ISSN
1027-4634
- Publication type
Article
- DOI
10.30970/ms.61.2.160-167