Abstract: In this paper, we proved transformation formulas for nonterminating very well-poised 4Φ3-series, 4Ψ4-series, 6Φ5-series, 6Ψ6-series, 8Φ7-series and 8Ψ8-series, which utilize the method of ...

Trigonometric sums and summation formulas have long served as essential tools for elucidating periodic phenomena across mathematics and the physical sciences. These techniques entail the explicit ...

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We obtain an expectation formula and give the probabilistic proofs of some summation and transformation formulas of q-series based on our expectation formula. Although these formulas in themselves are ...

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ABSTRACT: Very recently Atash and Al-Gonah [1] derived two extension formulas for Lauricella’s function of the second kind of several variables and . Now in this research paper we derive two families ...