The zeta-regularized product of odious numbers

Abstract

What is the product of all {\em odious} integers, i.e., of all integers whose binary expansion contains an odd number of $1$'s? Or more precisely, how to define a product of these integers which is not infinite, but still has a "reasonable" definition? We will answer this question by proving that this product is equal to ${\pi }^{1/4}\sqrt{2\phi e^{-\gamma }}$, where $\gamma$ and $\phi$ are respectively the Euler-Mascheroni and the Flajolet-Martin constants.

References in corpus (1)

• The regularized product of the Fibonacci numbers