论文标题
高转移功能的扰动的大型转移
Hypertranscendency of Perturbations of Hypertranscendental Functions
论文作者
论文摘要
受到银行在$γe^h $的高度递质工作的启发，其中$γ$是Euler gamma功能，$ h $是整个功能，我们调查何时ermoromoromormorormormorormorormormorormorormorormorormorormorormorormorormorormorormormorormorial ofermormorphic函数中$ f $和$ g $和$ g $和$ g $ andimplice and的复合物相比，$ fe^g。我们的结果（定理1和2）为银行的猜想（1977）提供了部分解决方案，以$γe^h $的高变量。我们还提供了一些足够的条件，以表格$ f+g $，$ f \ cdot g $和$ f \ circ g $在定理3和4中。
Inspired by the work of Bank on the hypertranscendence of $Γe^h$ where $Γ$ 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 $Γe^h$. We also give some sufficient conditions for hypertranscendence of meromorphic function of the form $f+g$, $f\cdot g$ and $f\circ g$ in Theorem 3 and 4.
