Bailey’s Transform, Lemma, Chains and Tree

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Positivity preserving transformations for $q$-binomial coefficients (2003, background): “The Bailey lemma is the following powerful mechanism for generating new Bailey pairs [6, 7, 9, 13, 41, 54].”
The WP‐Bailey Tree and its Implications (2001, methodology): “6), the resulting identity [5] is a well-known q-analog of Dougall’s summation formula due to Jackson: 8W7(a; ρ1, ρ2, a c , kq, q−n; q, q) = ( aq, kc , kρ1 a , kρ2 a )”
A Bailey Tree for Integrals (2003, methodology): “em 2 should have a series analogue as well which would lead to an elliptic Bailey tree for series (its analogue for q-hypergeometric series would be qualitatively diﬀerent from the tree considered in [1], [4]). As an illustration, we describe one particular sequence of identities generated by the de”
Inversions of integral operators and elliptic beta integrals on root systems (2004, background): “At the level of hypergeometric series — ordinary, basic or elliptic — the Bailey pair machinery allows for the derivation of infinite sequences of symmetry transformations [1, 2, 23, 27, 29].”
Essays on the theory of elliptic hypergeometric functions (2008, methodology): “LLIPTIC HYPERGEOMETRIC FUNCTIONS 27 6. Chains of symmetry transformations for functions Symmetry transformations for the plain and q-hypergeometric series are built with the help of the Bailey chains [1, 66]. This technique was generalized to the elliptic level in [52, 67]. Let us sketch this genera”