Simple Proofs Of Some Q-Series Identities

By using contiguous relations for basic hypergeometric series and mathematical induction, we give simple proofs of Bailey's ₄φ₃ summation, Carlitz's ₅φ₄ summation, Sears' ₃φ₂ to ₅φ₄ transformation, Sears' ₄φ₃ transformations,Chen's bibasic summation, Chu's bibasic symmetric transformation and Gasper's split poised ₁₀φ₉ transformationwhereλ= a²q/bcd.