Abel's method on summation by parts and terminating well-poised q-series identities

作者：Chu Wenchang^*; Jia Cangzhi

来源：Journal of Computational and Applied Mathematics, 2007, 207(2): 360-370.

DOI：10.1016/j.cam.2006.10.011

• Abel's lemma on summation by parts
• basic hypergeometric series
• terminating well-poised series

The Abel method on summation by parts is reformulated to present new and elementary proofs of several classical identities of terminating well-poised basic hypergeometric series, mainly discovered by [F H. Jackson, Certain q-identities, Quart. J. Math. Oxford Ser. 12 (1941) 167-172]. This strengthens further our conviction that as a traditional analytical instrument, the revised Abel method on summation by parts is indeed a very natural choice for working with basic hypergeometric series.

• 出版日期2007-10-15
• 单位大连理工大学