made with Mathematica technology MathWorld

Digit Product

Let s_b(n) be the sum of the base-b digits of n, and epsilon(n)=(-1)^(s_2(n)) the Thue-Morse sequence, then

 product_(n=0)^infty((2n+1)/(2n+2))^(epsilon(n))=1/2sqrt(2).

SEE ALSO: Digit, Digit Sum

REFERENCES:

Allouche, J.-P. "Series and Infinite Products Related to Binary Expansions of Integers." http://algo.inria.fr/seminars/sem92-93/allouche.ps.

Allouche, J.-P. and Cohen, H. "Dirichlet Series and Curious Infinite Products." Bull. London Math. Soc. 17, 531-538, 1985.

Shallit, J. O. "On Infinite Products Associated with Sums of Digits." J. Number Th. 21, 128-134, 1985.




CITE THIS AS:

Weisstein, Eric W. "Digit Product." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DigitProduct.html

The Wolfram Demonstrations Project Browse Topics View Latest
JUST RELEASED: Wolfram Mathematica 7