Jing GU , Zhizheng ZHANG . SOME NEW IDENTITIES OF ROGERS-RAMANUJAN TYPE^*[J]. Acta mathematica scientia, Series B, 2024 , 44(1) : 129 -142 . DOI: 10.1007/s10473-024-0106-2

[1] Gasper G, Rahman M. Basic Hypergeometric Series.Encyclopedia of Mathematics and its Applications. 2nd ed. Cambridge: Cambridge University Press, 1990
[2] Srivastava H M, Karlsson P W.Multiple Gaussian Hypergeometric Series. Ellis Horwood Series: Mathematics and Its Applications. New York: John Wiley & Sons Inc, 1985
[3] Gould H W, Hsu L C. Some new inverse series relations. Duke Math J, 1973, 40: 885-891
[4] Carlitz L. Some inverse relations. Duke Math J, 1973, 40: 893-901
[5] Chu W C. Gould-Hsu-Carlitz inversions and Rogers-Ramanujan identities. I. Acta Math Sinica, 1990, 33(1): 7-12
[6] Chu W C, Di Claudio L.Classical partition identities and basic hypergeometric series. Edizioni del Grifo, 2004
[7] Liu Z G. Carlitz inverses, the Rogers-Ramanujan identities and a quintuple product identity. Math Practice Theory, 1995(1): 70-74
[8] Hardy G H, Wright E M.An Introduction to the Theory of Numbers. Sixth ed. Oxford: Oxford University Press, 2008
[9] Ramanujan S.Collected papers of Srinivasa Ramanujan. Providence, RI: AMS Chelsea Publishing, 2000
[10] Rogers L J, Ramanujan S. Proof of certain identities in combinatory analysis [Proc Cambridge Philos Soc, 1919, 19: 214-216]//Collected Papers of Srinivasa Ramanujan. Providence, RI: AMS Chelsea Publ, 2000: 214-215
[11] Schur I. Ein Beitrag zur additiven Zahlentheorie und zur Theorie der KettenbrÜche. S.-B. Preuss. Klasse: Akad Wiss Phys Math, 1917: 302-321
[12] Bailey W N. A note on certain $q$-identities. Quart J Math, Oxford Ser, 1941, 12: 173-175
[13] Bailey W N. Some identities in combinatory analysis. Proc London Math Soc, 1947, 49(2): 421-425
[14] Slater L J. A new proof of Rogers's transformations of infinite series. Proc London Math Soc, 1951, 53(2): 460-475
[15] Slater L J. Further identities of the Rogers-Ramanujan type. Proc London Math Soc, 1952, 54(2): 147-167
[16] Bailey W N. Identities of the Rogers-Ramanujan type. Proc London Math Soc, 1948, 50(2): 1-10
[17] Chen X J, Chu W C. Carlitz inversions and identities of the Rogers-Ramanujan type. Rocky Mountain J Math, 2014, 44(4): 1125-1143
[18] Andrews G E. On the proofs of the Rogers-Ramanujan identities//$q$-Series and Partitions (Minneapolis, MN, 1988), IMA Vol Math Appl, 18. New York: Springer, 1989: 1-14
[19] Andrews G E.The Theory of Partitions. Cambridge: Cambridge University Press, 1998
[20] Berndt B C.Ramnaujan's Notebooks. Rart III. New York: Springer-Verlag, 1991
[21] Garrett K, Ismail M E H, Stanton D. Variants of the Rogers-Ramanujan identities. Adv Appl Math, 1999, 23(3): 274-299
[22] Ramanujan S. Problem 584. J Indian Math Soc, 1914, 6: 199-200
[23] Wang C, Chern S. Some basic hypergeometric transformations and Rogers-Ramanujan type identities. Integral Transforms Spec Funct, 2020, 31(11): 873-890
[24] Zhang Z Z, Jia Z Y. More Rogers-Ramanujan type identities. Proc Jangjeon Math Soc, 2012, 15(2): 215-225
[25] Zhang Z Z, Li X Q. A class of new $m$-mutlisum Rogers-Ramanujan identities and applications. Acta Math Sci, 2019, 39A(4): 851-864
[26] Andrews G E.Combinatorics and Ramanujan's “lost" notebook//Surveys in Combinatorics 1985
(Glasgow, 1985), London Math Soc Lecture Note Ser, 103. Cambridge: Cambridge University Press, 1985: 1-23
[27] Agarwal A K, Bressoud D M. Lattice paths and multiple basic hypergeometric series. Pacific J Math, 1989, 136(2): 209-228
[28] Rogers L J. On two theorems of combinatory analysis and some allied identities. Proc Lond Math Soc, 1917, 16: 315-336
[29] Heine E.Handbuch der Kugelfunctionen. Theorie und Anwendungen. Band I, II. Thesaurus Mathematicae, No. 1. WÜrzburg: Physica-Verlag, 1961
[30] Heine E. Über die Reihe ${1+\frac{(q^\alpha-1)(q^\beta-1)}{(q-1)(q^\gamma-1)}x+\frac{(q^\alpha-1)(q^{\alpha+1}-1)(q^\beta-1)(q^{\beta_1}-1)} {(q-1)(q^2-1)(q^\gamma-1)(q^{\gamma+1}-1)}+\cdots}$. (Aus einem Schreiben an Lejeune Dirichlet). J Reine Angew Math, 1846, 32: 210-212
[31] Slater L J. Generalized Hypergeometric Functions.Cambridge: Cambridge University Press, 1966
[32] Fine N J.Basic Hypergeometric Series and Applications. Providence, RI: American Mathematical Society, 1988
[33] Daum J A. The basic analogue of Kummer's theorem. Bull Amer Math Soc, 1942, 48: 711-713
[34] Andrews G E. On the $q$-analog of Kummer's theorem and applications. Duke Math J, 1973, 40: 525-528
[35] Kim Y S, Rathie A K, Lee C H. On $q$-analogue of Kummer's theorem and its contiguous results. Commun Korean Math Soc, 2003, 18: 151-157
[36] Kim Y S, Rathie A K, Choi J. Three-term contiguous functional relations for basic hypergeometric series ${{}_2\phi_1}$. Commun Korean Math Soc, 2005, 20(2): 395-403
[37] Harsh H V, Kim Y S, Rakha M A, Rathie A K. A study of $q$-contiguous function relations. Commun Korean Math Soc, 2016, 31(1): 65-94