Hypertranscendency of perturbations of hypertranscendental functions

[摘要] Inspired by the work of Bank on the hypertranscendence of Gamma e(h) where Gamma is the Euler gamma function and h is an entire function, we investigate when a meromorphic function fe(g) cannot satisfy any algebraic differential equation over certain field of meromorphic functions, where f and g are meromorphic and entire on the complex plane, respectively. Our results (Theorem 1 and 2) give partial solutions to Bank's Conjecture (1977) on the hypertranscendence of Gamma e(h). We also give some sufficient conditions for hypertranscendence of meromorphic function of the form f + g, f . g and f circle g in Theorem 3 and 4. (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-11-15

[关键词] Euler gamma function;Hypertranscendence;Algebraic differential equation