Two new transformation formulas for ${}_8{\psi }_8$ and ${}_8{W}_7$ series associated with Weierstrass' theta identity

Abstract

In this paper, we establish two new transformation formulas for ${}_8{\psi }_8$ and ${}_8{\varphi }_7$ 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 ${}_6{\psi }_6$ and Jackson's ${}_8{\varphi }_7$ summation formula.

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