数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (1): 129-142.doi: 10.1007/s10473-024-0106-2

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SOME NEW IDENTITIES OF ROGERS-RAMANUJAN TYPE*

Jing GU1,†, Zhizheng ZHANG2,3   

  1. 1. School of Mathematical Sciences, East China Normal University, Shanghai 200241, China;
    2. Department of Mathematics, Luoyang Normal University, Luoyang 471934, China;
    3. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453001, China
  • 收稿日期:2022-10-25 修回日期:2023-07-21 出版日期:2024-02-25 发布日期:2024-02-27
  • 通讯作者: † Jing GU, E-mail: 52215500005@stu.ecnu.edu.cn
  • 作者简介:Zhizheng ZHANG, E-mail: zhzhzhang-yang@163.com
  • 基金资助:
    National Natural Science Foundation of China (12271234)

SOME NEW IDENTITIES OF ROGERS-RAMANUJAN TYPE*

Jing GU1,†, Zhizheng ZHANG2,3   

  1. 1. School of Mathematical Sciences, East China Normal University, Shanghai 200241, China;
    2. Department of Mathematics, Luoyang Normal University, Luoyang 471934, China;
    3. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453001, China
  • Received:2022-10-25 Revised:2023-07-21 Online:2024-02-25 Published:2024-02-27
  • Contact: † Jing GU, E-mail: 52215500005@stu.ecnu.edu.cn
  • About author:Zhizheng ZHANG, E-mail: zhzhzhang-yang@163.com
  • Supported by:
    National Natural Science Foundation of China (12271234)

摘要: In this paper, we establish two transformation formulas for nonterminating basic hypergeometric series by using Carlitz's inversions formulas and Jackson's transformation formula. In terms of application, by specializing certain parameters in the two transformations, four Rogers-Ramanujan type identities associated with moduli 20 are obtained.

关键词: Carlitz's inversion, $q$-Series, Rogers-Ramanujan type identities

Abstract: In this paper, we establish two transformation formulas for nonterminating basic hypergeometric series by using Carlitz's inversions formulas and Jackson's transformation formula. In terms of application, by specializing certain parameters in the two transformations, four Rogers-Ramanujan type identities associated with moduli 20 are obtained.

Key words: Carlitz's inversion, $q$-Series, Rogers-Ramanujan type identities

中图分类号: 

  • 11B65