On zeros and deficiencies of differences of meromorphic functions

For a transcendental entire function f(z) in the complex plane, we study its divided differences Gn(z). We partially prove a conjecture posed by Bergweiler and Langley under the additional condition that the lower order of f (z) is smaller than 1/2. Furthermore, we prove that if zero is a deficient value of f (z), then delta(O,G) < 1, where G(z) = (f (z + c) - f(z))/f (z).Mathematics, AppliedMathematicsSCI(E)0ARTICLElongjianren2004@163.comnul