q-Binomial Theorem

Author

Eric W. Weisstein
December 7, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/q-BinomialTheorem.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/q-BinomialTheorem.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Sum

Sum[((QPochhammer[a,q,n])/(QPochhammer[q,q,n]))(z^n),{n,0,∞}]

TraditionalForm[%]

QHypergeometricPFQ[{a},{b},q,z]//TraditionalForm

FunctionExpand[%]

FullSimplify[((QPochhammer[a z,q])/(QPochhammer[z,q]))]

FullSimplify[((QPochhammer[a z,q])/(QPochhammer[z,q]))-QHypergeometricPFQ[{a},{},q,z]]