@article{SIGMA_2009_5_a49,
author = {Wenchang Chu and Chenying Wang},
title = {Partial {Sums} of {Two} {Quartic} $q${-Series}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2009},
volume = {5},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a49/}
}
Wenchang Chu; Chenying Wang. Partial Sums of Two Quartic $q$-Series. Symmetry, integrability and geometry: methods and applications, Tome 5 (2009). http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a49/
[1] Andrews G. E., “Three aspects of partitions”, Séminaire Lotharingien de Combinatoire (Salzburg, 1990), Publ. Inst. Rech. Math. Av., 462, Univ. Louis Pasteur, Strasbourg, 1991, 5–18 | MR
[2] Andrews G. E., Askey R., Roy R., Special functions, Encyclopedia of Mathematics and Its Applications, 71, Cambridge University Press, Cambridge, 1999 | MR | Zbl
[3] Bailey W. N., “Well-poised basic hypergeometric series”, Quart. J. Math. Oxford Ser., 18 (1947), 157–166 | DOI | MR | Zbl
[4] Chu W., “Inversion techniques and combinatorial identities: Jackson's $q$-analogue of the Dougall–Dixon theorem and the dual formulae”, Compositio Math., 95 (1995), 43–68 | MR | Zbl
[5] Chu W., “Abel's lemma on summation by parts and basic hypergeometric series”, Adv. in Appl. Math., 39 (2007), 490–514 | DOI | MR | Zbl
[6] Chu W., Jia C., “Abel's method on summation by parts and theta hypergeometric series”, J. Combin. Theory Ser. A, 115 (2008), 815–844 | DOI | MR | Zbl
[7] Chu W., Wang C., “Abel's lemma on summation by parts and partial $q$-series transformations”, Sci. China Ser. A, 52 (2009), 720–748 | DOI | MR | Zbl
[8] Chu W., Wang X., “Abel's lemma on summation by parts and terminating $q$-series identities”, Numer. Algorithms, 49 (2008), 105–128 | DOI | MR | Zbl
[9] Frenkel I. B., Turaev V. G., “Elliptic solutions of the Yang–Baxter equation and modular hypergeometric functions”, The Arnold–Gelfand Mathematical Seminars, Birkhäuser Boston, Boston, MA, 1997, 171–204 | MR | Zbl
[10] Gasper G., “Summation, transformation, and expansion formulas for bibasic series”, Trans. Amer. Math. Soc., 312 (1989), 257–277 | DOI | MR | Zbl
[11] Gasper G., Rahman M., “An indefinite bibasic summation formula and some quadratic, cubic and quartic summation and transformation formulas”, Canad. J. Math., 42 (1990), 1–27 | MR | Zbl
[12] Gasper G., Rahman M., Basic hypergeometric series, 2nd ed., Encyclopedia of Mathematics and Its Applications, 96, Cambridge University Press, Cambridge, 2004 | MR | Zbl
[13] Gessel I., Stanton D., “Applications of $q$-Lagrange inversion to basic hypergeometric series”, Trans. Amer. Math. Soc., 277 (1983), 173–201 | DOI | MR | Zbl
[14] Ismail M. E. H., Stanton D., “Tribasic integrals and identities of Rogers–Ramanujan type”, Trans. Amer. Math. Soc., 355 (2003), 4061–4091 | DOI | MR | Zbl
[15] Koornwinder T. H., “Askey–Wilson polynomials as zonal spherical functions on the $\mathrm{SU}(2)$ quantum group”, SIAM J. Math. Anal., 24 (1993), 795–813 | DOI | MR | Zbl
[16] Rahman M., “Some quadratic and cubic summation formulas for basic hypergeometric series”, Canad. J. Math., 45 (1993), 394–411 | MR | Zbl
[17] Rahman M., Verma A., “Quadratic transformation formulas for basic hypergeometric series”, Trans. Amer. Math. Soc., 335 (1993), 277–302 | DOI | MR | Zbl
[18] Stanton D., “The Bailey–Rogers–Ramanujan group”, $q$-series with applications to combinatorics, number theory, and physics, Contemp. Math., 291, 2001, 55–70 | MR | Zbl
[19] Stromberg K. R., An introduction to classical real analysis, Wadsworth International Mathematics Series, Wadsworth International, Belmont, Calif., 1981 | MR | Zbl
[20] Warnaar S. O., “Summation and transformation formulas for elliptic hypergeometric series”, Constr. Approx., 18 (2002), 479–502 ; math.QA/0001006 | DOI | MR | Zbl