English

Some Implications of the WP-Bailey Tree

Number Theory 2019-01-16 v1

Abstract

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\\ (αn(a,k)(\alpha_n(a,k), βn(a,k))\beta_n(a,k)), in which αn(a,k)\alpha_n(a,k) is independent of kk, for generalizations of identities of the Rogers-Ramanujan type.

Cite

@article{arxiv.1901.04840,
  title  = {Some Implications of the WP-Bailey Tree},
  author = {James Mc Laughlin and Peter Zimmer},
  journal= {arXiv preprint arXiv:1901.04840},
  year   = {2019}
}

Comments

17 pages

R2 v1 2026-06-23T07:12:22.826Z