Two new transformation formulas for ${}_{8}ψ_{8}$ and ${}_{8}W_{7}$ series associated with Weierstrass' theta identity

In this paper, we establish two new transformation formulas for ${}_{8}ψ_{8}$ and ${}_8ϕ_7$ series by means of Slater's general transformation for bilateral series. As applications, some specific transformation formulas are presented among which include a general form of Weierstrass' theta identity and new proofs of Bailey's VWP ${}_6ψ_6$ and Jackson's ${}_8ϕ_7$ summation formula.

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