论文标题
与$ \ pm 1 $ thue-morse序列相关的先验无限产品
Transcendental Infinite Products Associated with the $\pm 1$ Thue-Morse Sequence
论文作者
论文摘要
几位作者研究了与$ \ pm 1 $ thue-morse序列相关的无限产品，其价值是理性或代数非理性的。在此简短说明中，我们证明了三个新的无限产品标识，涉及$π$，$ \ sqrt {2} $和$ \ pm 1 $ thue-morse序列，这是由Allouche，riasat和Shallit的结果建立的。然后，我们使用我们的方法来找到在Flajolet-Martin常数中出现的产品的新表达式。
Infinite products associated with the $\pm 1$ Thue-Morse sequence whose value is rational or algebraic irrational have been studied by several authors. In this short note we prove three new infinite product identities involving $π$, $\sqrt{2}$, and the $\pm 1$ Thue-Morse sequence, building on a result by Allouche, Riasat, and Shallit. We then use our method to find a new expression for a product appearing within the context of the Flajolet-Martin constant.
