-Abel's theorem is the following q-series
identity.
![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/Inline2.svg)
is a q-binomial coefficient.
q-Abel's Theorem
See also
Abel's Binomial TheoremExplore with Wolfram|Alpha
References
Bhatnagar, G. "Inverse Relations, Generalized Bibasic Series, and Their
Extensions." PhD thesis. Columbus, OH: 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 Resource. https://mathworld.wolfram.com/q-AbelsTheorem.html