论文标题
$ ϕ $ - 摩尔斯序列和无限产品
$ϕ$-Thue-Morse sequences and infinite products
论文作者
论文摘要
在本文中，我们介绍了一种新方法，以计算由涉及thue-morse序列的自动序列定义的无限产品。作为示例，对于任何正整数$ q $和$ r $ $ \ prod_ {n = 0}^{\ infty} r（n）^{\ frac {1+a_n} {2}} {2}} s（n）^{\ frac {\ frac {1-a_n} {2} {2} {2}} = 2cos（ \ in \ in \ mathbf {n}} $是以$ a_0 = 1，a_1 = -1 $开头的thue -morse序列。
In this article we introduce a new approach to compute infinite products defined by automatic sequences involving the Thue-Morse sequence. As examples, for any positive integers $q$ and $r$ such that $0 \leq r \leq q-1$, we find infinitely many couples of rational functions $R(x)$ and $S(n)$ such that $$\prod_{n=0}^{\infty}R(n)^{\frac{1+a_n}{2}}S(n)^{\frac{1-a_n}{2}}=2cos(\frac{2r+1}{2q}π),$$ where $(a_n)_{n \in \mathbf{N}}$ is the Thue-Morse sequence beginning with $a_0=1,a_1= -1$.
