Unicity of transcendental meromorphic functions concerning differential-difference polynomials

Let f and g be two transcendental meromorphic functions of finite order with a Borel exceptional value infinity, let alpha (not equivalent to 0) be a small function of both f and g, let d, k, n, m and v(j)(j = 1, 2, ..., d) be positive integers, and let c(j)(j = 1, 2, ..., d) be distinct nonzero finite values. If n >= max{2k + m + sigma + 5,sigma + 2d + 3), where sigma = v(1) + v(2) + ... + v(d), and (f(n)(z)(f(m)(z) - 1) Pi(d)(j=1) f(vj)(z + c(j)))((k)) and (g(n)(z)(g(m)(z) - 1) Pi(d)(j=1) g(vj)(z + c(j)))((k)) share alpha CM then f tg, where t(m) = t(n+sigma) = 1. This result extends and improves some restlts due to [0, 14, 15, 9].

Automated summary

The paragraph discusses the properties and conditions of two transcendental meromorphic functions, as well as their relationship under certain conditions. It extends and improves previous results in the field.