![sum_(y=0)^m(-1)^(m-y)q^((m-y; 2))[m; y]_q(1-wq^m)/(q-wq^y)
×(1-wq^y)^m(-(1-z)/(1-wq^y);q)_y
=(1-z)^mq^((m; 2)),](/images/equations/q-AbelsTheorem/NumberedEquation1.svg) |
where ![[n; y]_q](/images/equations/q-AbelsTheorem/Inline1.svg)
is a q-binomial coefficient.
q-Abel's Theorem
See also
Abel's Binomial TheoremReferences
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 TheoremCite this as:
Weisstein, Eric W. "q-Abel's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/q-AbelsTheorem.html