Infinite products with strongly $B$-multiplicative exponents

Details Infinite products with strongly $B$-multiplicative exponents Infinite products with strongly $B$-multiplicative exponents

2007-09-26

arxiv.org/abs/0709.4031v2

Annales Univ. Sci. Budapest. Sect. Comput. 28 (2008) 35-53. Errata 32 (2010) 253

Mathematics

Number Theory

Updated [14] and journal reference

Scientific paper

Let $N_{1,B}(n)$ denote the number of ones in the $B$-ary expansion of an integer $n$. Woods introduced the infinite product $P :=\prod_{n \geq 0} (\frac{2n+1}{2n+2})^{(-1)^{N_{1,2}(n)}}$ and Robbins proved that $P = 1/\sqrt{2}$. Related products were studied by several authors. We show that a trick for proving that $P^2 = 1/2$ (knowing that $P$ converges) can be extended to evaluating new products with (generalized) strongly $B$-multiplicative exponents. A simple example is $$ \prod_{n \geq 0} (\frac{Bn+1}{Bn+2})^{(-1)^{N_{1,B}(n)}} = \frac{1}{\sqrt B}. $$

Affiliated with

Also associated with

No associations

Rating

Infinite products with strongly $B$-multiplicative exponents does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Infinite products with strongly $B$-multiplicative exponents, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Infinite products with strongly $B$-multiplicative exponents will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-693894