Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 5 (2009), 050, 19 pages      arXiv:0904.3453      http://dx.doi.org/10.3842/SIGMA.2009.050

Partial Sums of Two Quartic q-Series

Wenchang Chu a and Chenying Wang b
a) Dipartimento di Matematica, Università degli Studi di Salento, Lecce-Arnesano P. O. Box 193, Lecce 73100, Italy
b) College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China

Received January 20, 2009, in final form April 17, 2009; Published online April 22, 2009

Abstract
The partial sums of two quartic basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several summation and transformation formulae are consequently established.

Key words: basic hypergeometric series (q-series); well-poised q-series; quadratic q-series; cubic q-series; quartic q-series; the modified Abel lemma on summation by parts.

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