Journal of East China Normal University(Natural Science) >

2015 , Vol. 2015 >Issue 6: 46 - 52

DOI: https://doi.org/10.3969/j.issn.1000-5641.2015.06.007

Article

New transformation for the partial sum of a cubic q-series

  • WANG Chen-Ying
Expand

Received date: 2015-04-24

  Online published: 2015-12-23

Fold

Abstract

The partial sum of a cubic basic hypergeometric series is investigated by means of the modified Abel's lemma on summation by
parts. A new transformation formula for the cubic series is established, which expands some known cubic q-series summation
formulae.

Cite this article

WANG Chen-Ying . New transformation for the partial sum of a cubic q-series[J]. Journal of East China Normal University(Natural Science), 2015 , 2015(6) : 46 -52 . DOI: 10.3969/j.issn.1000-5641.2015.06.007

References

[1]CHU W, WANG C. Abel's lemma on summation by parts and partialq-series transformations [J]. Science in China Ser A, 2009, 52(4):720-748.
[2] GASPER G, RAHMAN M.Basic Hypergeometric Series [M]. Cambridge: Cambridge University Press, 2004.
[3] SLATER L J.Generalized Hypergeometric Functions [M]. Cambridge: CambridgeUniversity Press, 1966.
[4] CHU W.Inversion techniques and combinatorial identities [J]. Bollettino UM I, 1993(7): 737-760.
[5] CHU W.Inversion techniques and combinatorial identities: Jackson's $q$-analogue of the Dougall-Dixon theorem and the dual formulae [J].Compositio Mathematica, 1995, 95(1): 43-68.
[6] GASPER G.Summation, transformation, and expansion formulas for bibasic series[J]. Trans Amer Math Soc, 1989, 312(1): 257-277.
[7] GASPER G, RAHMAN M.An indefinite bibasic summation formula and some quadratic, cubic and quartic summation and transformation formulas [J].Can J Math 1990, 42: 1-27.
Options
Outlines

/

〈 〉