q-Abel's Theorem

 sum_(y=0)^m(-1)^(m-y)q^((m-y; 2))[m; y]_q(1-wq^m)/(q-wq^y) 
=(1-z)^mq^((m; 2)),

where [n; y]_q is a q-binomial coefficient.

See also

Abel's Binomial Theorem


Bhatnagar, G. Inverse Relations, Generalized Bibasic Series, and their U(n) Extensions. Ph.D. thesis. Ohio State University, p. 105, 1995.Chu, W. C. and Hsu, L. C. "Some New Applications of Gould-Hsu Inversions." J. Combin. Inform. System Sci. 14, 1-4, 1989.

Referenced on Wolfram|Alpha

q-Abel's Theorem

Cite this as:

Weisstein, Eric W. "q-Abel's Theorem." From MathWorld--A Wolfram Web Resource.