88 research outputs found
Some Applications of a Bailey-type Transformation
If k is set equal to aq in the definition of a WP Bailey pair, βn(a, k) = Xn j=0 (k/a)n−j (k)n+j (q)n−j (aq)n+j αj (a, k), this equation reduces to βn = Pn j=0 αj . This seemingly trivial relation connecting the αn’s with the βn’s has some interesting consequences, including several basic hypergeometric summation formulae, a connection to the Prouhet-Tarry-Escott problem, some new identities of the Rogers-Ramanujan-Slater type, some new expressions for false theta series as basic hypergeometric series, and new transformation formulae for poly-basic hypergeometric series
Some Implications of the WP-Bailey Tree
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 new transformations for basic hypergeometric series. Finally, we briefly consider the implications of WP-Bailey pairs (αn(a, k), βn(a, k)), in which αn(a, k) is independent of k, for generalizations of identities of the Rogers-Ramanujan type
Hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions
In this paper, we investigate the relationships among hypergeometric series,
truncated hypergeometric series, and Gaussian hypergeometric functions through
some families of `hypergeometric' algebraic varieties that are higher
dimensional analogues of Legendre curves.Comment: 25 page
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