A NEW SUMMATION FORMULA FOR WP-BAILEY PAIRS

作者：Mc Laughlin James^*

来源：Applicable Analysis and Discrete Mathematics, 2011, 5(1): 67-79.

DOI：10.2298/AADM110203004M

• Bailey pairs
• WP-Bailey chains
• WP-Bailey pairs
• Lambert series
• basic hypergeometric series

Let (alpha(n)(a, k), beta(n)(a, k)) be a WP-Bailey pair. Assuming the limits exist, let
(alpha(n)*(a), beta(n)*(a))(n >= 1) = lim(k-->1) (alpha(n)(a, k), beta(n)(a, k)/1 - k)(n >= 1)
be the derived WP-Bailey pair. By considering a particular limiting case of a transformation due to George Andrews, we derive new basic hypergeometric summation and transformation formulae involving derived WP-Bailey pairs. We then use these formulae to derive new identities for various theta series/products which are expressible in terms of certain types of Lambert series.

• 出版日期2011-4