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Abstract
Basic hypergeometric series, or q-series, play a fundamental role in many areas of mathematics, including combinatorics, number theory, and mathematical physics. The study of their transformation formulas provides deep insights into the interrelations among various classes of these series. This paper investigates several transformation formulas that establish connections between different forms of basic hypergeometric series. By employing classical results on transformations, new relations and identities among terminating and non-terminating q-series are derived. The approach unifies several known results and extends them to more generalized parameter domains. The obtained transformations not only simplify the evaluation of certain q-series but also reveal structural symmetries underlying their behavior. These findings contribute to the broader theory of basic hypergeometric functions and open avenues for applications in partition theory, special functions, and other analytical studies involving q-analogues.
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References
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