Further Applications of the $$\boldsymbol{G}$$ Function Integral Method

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In our recent work we proposed a generalization of the beta integral method for derivation of the hypergeometric identities which can by analogy be termed ‘‘the G function integral method’’. In this paper we apply this technique to the cubic and the degenerate Miller–Paris transformations to get several new transformation and summation formulas for the generalized hypergeometric functions at a fixed argument. We further present an alternative approach for reducing the right hand sides resulting from our method to a single hypergeometric function which does not require the use of summation formulas.