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Cauchy Binomial Theorem


product_(k=1)^(n)(1+yq^k)=sum_(m=0)^(n)y^mq^(m(m+1)/2)[n; m]_q
(1)
=sum_(m=0)^(n)y^mq^(m(m+1)/2)((q)_n)/((q)_m(q)_(n-m)),
(2)

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


See also

q-Binomial Coefficient, q-Binomial Theorem

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Cite this as:

Weisstein, Eric W. "Cauchy Binomial Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CauchyBinomialTheorem.html

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