关于多项式、幂和第n个素函数的非完整character
On the non-holonomic character of logarithms, powers, and the n-th prime function
摘要：
我们建立了由整数的幂和“分数”幂形成的序列以及素数序列是非完整的，从而回答了Gerhold的三个公开问题[Electronic Journal of Combinatorics 11（2004），R87]。我们的证明依赖于基本的复分析，即连接的结构定理的奇异性的解决方案，线性微分方程和阿贝尔定理。简要讨论了基于奇异性的方法的范围，并证明了几个自然发生的序列是非完整的。
英文摘要：
We establish that the sequences formed by logarithms and by "fractional" powers of integers, as well as the sequence of prime numbers, are non-holonomic, thereby answering three open problems of Gerhold [Electronic Journal of Combinatorics 11 (2004), R87]. Our proofs depend on basic complex analysis, namely a conjunction of the Structure Theorem for singularities of solutions to linear differential equations and of an Abelian theorem. A brief discussion is offered regarding the scope of singularity-based methods and several naturally occurring sequences are proved to be non-holonomic.
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