In this paper, we give an extension of the first Heine's transformation formula using $q$-difference equations. Further, we discussed a Ramanujan's theta function $\psi(q)$ and deduced it as a particular case.
Keywords and Phrases
$q$-Difference operator; $q$-Binomial theorem; $q$-integral identities; $q$-Difference equations, Ramanujan theta function.
A.M.S. subject classiﬁcation
05A30, 11B65, 33D15, 33D60, 39A13.