Geodesic
Rogers–Ramanujan Type Identities Involving Double Sums
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove four new Rogers–Ramanujan-type identities for double series. They follow from the classical Rogers–Ramanujan identities using the constant term method and properties of Rogers–Szegő polynomials.
Keywords: Rogers–Ramanujan type identities, sum-product identities, constant term method. 
@article{SIGMA_2024_20_a102,
     author = {Dandan Chen and Siyu Yin},
     title = {Rogers{\textendash}Ramanujan {Type} {Identities} {Involving} {Double} {Sums}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2024},
     volume = {20},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a102/}
}
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Dandan Chen; Siyu Yin. Rogers–Ramanujan Type Identities Involving Double Sums. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a102/

[1] Andrews G.E., $q$-series: their development and application in analysis, number theory, combinatorics, physics, and computer algebra, CBMS Reg. Conf. Ser. Math., 66, American Mathematical Society, Providence, RI, 1986 | DOI | MR | Zbl

[2] Andrews G.E., Uncu A.K., “Sequences in overpartitions”, Ramanujan J., 61 (2023), 715–729, arXiv: 2111.15003 | DOI | MR | Zbl

[3] Berkovich A., Warnaar S.O., “Positivity preserving transformations for $q$-binomial coefficients”, Trans. Amer. Math. Soc., 357 (2005), 2291–2351, arXiv: math.CO/0302320 | DOI | MR | Zbl

[4] Cao Z., Wang L., “Multi-sum Rogers–Ramanujan type identities”, J. Math. Anal. Appl., 522 (2023), 126960, 24 pp., arXiv: 2205.12786 | DOI | MR | Zbl

[5] Chern S., “Asymmetric Rogers–Ramanujan type identities. I The Andrews–Uncu conjecture”, Proc. Amer. Math. Soc., 151 (2023), 3269–3279, arXiv: 2203.15168 | DOI | MR | Zbl

[6] Gasper G., Rahman M., Basic hypergeometric series, Encyclopedia Math. Appl., 96, 2nd ed., Cambridge University Press, Cambridge, 2004 | DOI | MR | Zbl

[7] Nahm W., “Conformal field theory, dilogarithms, and three-dimensional manifolds”, Adv. Appl. Clifford Algebras, 4 (1994), 179–191 | MR

[8] Nahm W., “Conformal field theory and the dilogarithm”, XIth International Congress of Mathematical Physics (Paris, 1994), International Press, Cambridge, MA, 1995, 662–667 | MR | Zbl

[9] Nahm W., “Conformal field theory and torsion elements of the Bloch group”, Frontiers in Number Theory, Physics, and Geometry. II, Springer, Berlin, 2007, 67–132, arXiv: hep-th/0404120 | DOI | MR | Zbl

[10] Rogers L.J., “Second memoir on the expansion of certain infinite products”, Proc. Lond. Math. Soc., 25 (1893), 318–343 | DOI | MR

[11] Wang L., “New proofs of some double sum Rogers–Ramanujan type identities”, Ramanujan J., 62 (2023), 251–272, arXiv: 2203.15572 | DOI | MR | Zbl

[12] Wang L., “Explicit forms and proofs of Zagier's rank three examples for Nahm's problem”, Adv. Math., 450 (2024), 109743, 46 pp., arXiv: 2211.04375 | DOI | MR | Zbl

[13] Zagier D., “The dilogarithm function”, Frontiers in Number Theory, Physics, and Geometry. II, Springer, Berlin, 2007, 3–65 | DOI | MR | Zbl