** Abstract: **
We present a technique of
deriving basic hypergeometric identities from their
specializations with a fewer number of parameters
by using the classical Cauchy identity on the expansion
of the power of *x* in terms of the *q*-binomial coefficients.
We call method the Cauchy augmentation. Despite its
simple appearance, the Cauchy identity
plays a marvelous role for parameter augmentation.
For example, from
the Euler identity one can reach
the *q*-Gauss summation formula by using the
Cauchy augmentation twice. This idea also applies to Jackson's to transformation formula. Moreover, we obtain a transformation formula
analogous to Jackson's formula.
** AMS Classification:** 05A30,33D15.
** Keywords:**
Cauchy augmentation, Euler identity, Cauchy identity, Gauss
identity, basic hypergeometric series, Jackson's transformation
formula.
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