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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Volume 276, Pages 27–38 (Mi tm3362)  
This article is cited in 39 scientific papers (total in 39 papers)

q-Orthogonal polynomials, Rogers–Ramanujan identities, and mock theta functions

George E. Andrews

Department of Mathematics, The Pennsylvania State University, University Park, PA, USA
Full-text PDF (181 kB) Citations (39)
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Abstract: In this paper, we examine the role that q-orthogonal polynomials can play in the application of Bailey pairs. The use of specializations of q-orthogonal polynomials reveals new instances of mock theta functions.
Received in November 2010
English version:
Proceedings of the Steklov Institute of Mathematics, 2012, Volume 276, Pages 21–32
DOI: https://doi.org/10.1134/S0081543812010038
Bibliographic databases:
Document Type: Article
UDC: 517.538.3
Language: English
Citation: George E. Andrews, “q-Orthogonal polynomials, Rogers–Ramanujan identities, and mock theta functions”, Number theory, algebra, and analysis, Collected papers. Dedicated to Professor Anatolii Alekseevich Karatsuba on the occasion of his 75th birthday, Trudy Mat. Inst. Steklova, 276, MAIK Nauka/Interperiodica, Moscow, 2012, 27–38; Proc. Steklov Inst. Math., 276 (2012), 21–32
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tm3362
  • https://www.mathnet.ru/eng/tm/v276/p27
    • This publication is cited in the following 39 articles:
    1. Olivia Yao, “Rogers-Ramanujan type identities and Chebyshev polynomials”, Proc. Amer. Math. Soc., 153:3 (2025), 1215  crossref
    2. Bing He, “Hecke-type series involving infinite products”, European Journal of Combinatorics, 120 (2024), 103959  crossref
    3. J. G. Bradley-Thrush, “Evaluation of Hecke–Rogers series and expansions of the rank function”, Ramanujan J, 2024  crossref
    4. Su-Ping Cui, Hai-Xing Du, Nancy S. S. Gu, Liuquan Wang, “Hecke-type double sums and the Bailey transform”, Ramanujan J, 2024  crossref
    5. Su-Ping Cui, Nancy S. S. Gu, Chen-Yang Su, Matthew H. Y. Xie, “Generalizations of mock theta functions”, Int. J. Number Theory, 20:09 (2024), 2395  crossref
    6. Zhi-Guo Liu, “On a Transformation of Triple $q$-Series and Rogers–Hecke Type Series”, SIGMA, 20 (2024), 086, 37 pp.  mathnet  crossref
    7. Lisa H. Sun, “Rogers–Ramanujan type identities and Chebyshev polynomials of the third kind”, Ramanujan J, 60:3 (2023), 761  crossref
    8. Chuanan Wei, Yuanbo Yu, Qiuxia Hu, “Two generalizations of Jacobi's triple product identity and their applications”, Ramanujan J, 60:4 (2023), 925  crossref
    9. Su-Ping Cui, Nancy S. S. Gu, Dazhao Tang, “Generalizations of Mock Theta Functions and Appell–Lerch Sums”, Bull. Iran. Math. Soc., 49:5 (2023)  crossref
    10. Ying Zhang, Wenlong Zhang, Jingjing Zhang, “Several q-series transformation formulas and new Hecke–Rogers type series identities”, Ramanujan J, 60:3 (2023), 627  crossref
    11. Zhiguo Liu, “A multiple q-exponential differential operational identity”, Acta Math Sci, 43:6 (2023), 2449  crossref
    12. Eric T. Mortenson, Ankit Sahu, “Expressing q-series in terms of building blocks of Hecke-type double-sums”, Int. J. Number Theory, 19:06 (2023), 1429  crossref
    13. Lovejoy J., “Bailey Pairs and Indefinite Quadratic Forms, II. False Indefinite Theta Functions”, Res. Number Theory, 8:2 (2022), 24  crossref  mathscinet  isi  scopus
    14. Su-Ping Cui, Nancy S.S. Gu, Qing-Hu Hou, Chen-Yang Su, “Three-parameter mock theta functions”, Journal of Mathematical Analysis and Applications, 515:2 (2022), 126459  crossref
    15. Qiuxia Hu, Bilal Khan, Serkan Araci, Mehmet Acikgoz, “New double-sum expansions for certain Mock theta functions”, MATH, 7:9 (2022), 17225  crossref
    16. Liu Zh.-G., “On the Askey-Wilson Polynomials and a Q-Beta Integral”, Proc. Amer. Math. Soc., 149:11 (2021), 4639–4648  crossref  mathscinet  isi  scopus
    17. Cui S.-P., Gu N.S.S., “Some New Mock Theta Functions”, Adv. Appl. Math., 131 (2021), 102267  crossref  mathscinet  isi
    18. Patkowski A.E., “A General Double Sum Identity, Mock Theta Functions, and Bailey Pairs”, Acta Arith., 198:4 (2021), 377–385  crossref  mathscinet  isi
    19. Jia Z., Khan B., Hu Q., Niu D., “Applications of Generalized Q-Difference Equations For General Q-Polynomials”, Symmetry-Basel, 13:7 (2021), 1222  crossref  isi
    20. Andrews G.E., Berndt B.C., Chan S.H., Kim S., Malik A., “Four Identities For Third Order Mock Theta Functions”, Nagoya Math. J., 239 (2020), PII S0027763018000351, 173–204  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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