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

In this paper, we establish two new transformation formulas for ${}_{8}psi_{8}$ and ${}_8phi_7$ series by means of Slaters 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 Baileys VWP ${}_6psi_6$ and Jacksons ${}_8phi_7$ summation formula.