Aq-analog of Euler's decomposition formula for the double zeta function

David M. Bradley
2005 International Journal of Mathematics and Mathematical Sciences  
The double zeta function was first studied by Euler in response to a letter from Goldbach in 1742. One of Euler's results for this function is a decomposition formula, which expresses the product of two values of the Riemann zeta function as a finite sum of double zeta values involving binomial coefficients. Here, we establish aq-analog of Euler's decomposition formula. More specifically, we show that Euler's decomposition formula can be extended to what might be referred to as a "doubleq-zeta
more » ... as a "doubleq-zeta function" in such a way that Euler's formula is recovered in the limit asqtends to 1.
doi:10.1155/ijmms.2005.3453 fatcat:lrjs4pundjburiebp2kcjmhp5q