Parameter Augmentation for Two Formulas

In this paper, by using the q-exponential operator technique on the q-integral form of the Sears transformation formula and a Gasper q-integral formula, we obtain their generalizations. 1 Notation In this paper, we follow the notation and terminology in ([4]). For a real or complex number q (|q| < 1). let (λ)∞ = (λ; q)∞ = ∞ ∏ n=1 (1 − aq); (1.1) and let (λ : q)μ be defined by (λ)μ = (λ; q)μ = (λ; q)∞ (λqμ; q)∞ for arbitrary parameters λ and μ, so that (λ)n = (λ; q)n = { 1, n=0 (1−λ)(1−λq)...(1−λq), (n∈N=1,2,3,···) The q-binomial coefficient is defined by [ n k ] = (q)n (q)k(q)n−k Further, recall the definition of basic hypergeometric series, sφs−1 [ α1, · · · , αs β1, · · · , βs−1 ∣