The Cauchy binomial theorem states that
 |  | ![sum_(m=0)^(n)y^mq^(m(m+1)/2)[n; m]_q](/images/equations/CauchyBinomialTheorem/Inline3.svg) |
(1)
|
 |  |  |
(2)
|
where ![[n; m]_q](/images/equations/CauchyBinomialTheorem/Inline7.svg)
is a q-binomial coefficient.
Cauchy Binomial Theorem
See also
q-Binomial Coefficient, q-Binomial TheoremExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Cauchy Binomial Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CauchyBinomialTheorem.html