Some Implications of the WP-Bailey Tree
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🧮 math.NT
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wp-baileyderivealphabasicconsiderhypergeometricimplicationspairs
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We consider a special case of a WP-Bailey chain of George Andrews, and use it to derive a number of curious transformations of basic hypergeometric series. We also derive two new WP-Bailey pairs, and use them to derive some additional new transformations for basic hypergeometric series. Finally, we briefly consider the implications of WP-Bailey pairs\\ $(\alpha_n(a,k)$, $\beta_n(a,k))$, in which $\alpha_n(a,k)$ is independent of $k$, for generalizations of identities of the Rogers-Ramanujan type.
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