## q-Binomial Theorem

The q-Analog of the Binomial Theorem

is given by

Written as a q-Series, the identity becomes

where

(Heine 1847, p. 303; Andrews 1986). The Cauchy Binomial Theorem is a special case of this general theorem.

See also Binomial Series, Binomial Theorem, Cauchy Binomial Theorem, Heine Hypergeometric Series, Ramanujan Psi Sum

References

Andrews, G. E. -Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra. Providence, RI: Amer. Math. Soc., p. 10, 1986.

Heine, E. Untersuchungen über die Reihe .'' J. reine angew. Math. 34, 285-328, 1847.