论文标题
元C-FINITE ANSATZ
The Meta-C-finite Ansatz
论文作者
论文摘要
fibonacci编号满足著名的复发$ f_n = f_ {n -1} + f_ {n -2} $。 C-Finite序列的理论可确保fibonacci数字由$ m $（即$ f_ {mn} $）排除，即满足每个正整数$ m $的类似复发，并且这些复发具有显式，均匀的表示。我们将证明$ a（mn）$对于任何C-Finite序列$ a（n）$具有均超过$ m $的均匀复发，并使用它自动获得一些著名的总和身份。
The Fibonacci numbers satisfy the famous recurrence $F_n = F_{n - 1} + F_{n - 2}$. The theory of C-finite sequences ensures that the Fibonacci numbers whose indices are divisible by $m$, namely $F_{mn}$, satisfy a similar recurrence for every positive integer $m$, and these recurrences have an explicit, uniform representation. We will show that $a(mn)$ has a uniform recurrence over $m$ for any C-finite sequence $a(n)$ and use this to automatically derive some famous summation identities.
