关于Rogers-Ramanujan型连分数的一类新构造
A New Class of Rogers-Ramanujan Type Continued Fractions
摘要: 拉马努金笔记本中记载的 Rogers-Ramanujan连分数具有重要研究价值。本文以两个 Rogers恒等式为出发点，利用数学归纳法及新递推公式，构造出一种新的 Rogers-Ramanujan型连分数。
Abstract: The Rogers-Ramanujan continued fraction, as recorded in Ramanujan’s Notebooks, possesses significant research value. Starting from the two Rogers identities, this paper constructs a new Rogers-Ramanujan type continued fraction by means of mathematical induction and newly derived recurrence relations.
文章引用：吕白雪. 关于Rogers-Ramanujan型连分数的一类新构造[J]. 理论数学, 2026, 16(5): 7-15. https://doi.org/10.12677/PM.2026.165126

参考文献

[1] Andrews, G.E. (1981) Ramunujan’s “Lost” Notebook III. The Rogers-Ramanujan Continued Fraction. Advances in Mathematics, 41, 186-208. [Google Scholar] [CrossRef] 
[2] Prodinger, H. (2010) Continued Fraction Expansions for Q-Tangent and Q-Cotangent Functions. Discrete Mathematics Theoretical Computer Science, 12, 47-64. [Google Scholar] [CrossRef] 
[3] Gu, N.S.S. and Prodinger, H. (2011) On Some Continued Fraction Expansions of the Rogers- Ramanujan Type. The Ramanujan Journal, 26, 323-367.[CrossRef] 
[4] 张英凡.Rogers-Ramanujan型连分数的构造及其模等式[D]:[硕士学位论文].重庆:重庆师范 大学，2025.
[5] 蔡华蓉.Rogers-Ramanujan型连分数的构造方法D]:[硕士学位论文].重庆:重庆师范大学， 2024.
[6] Rogers, L.J. (1893) Second Memoir on the Expansion of Certain Infinite Products. Proceedings of the London Mathematical Society, 1, 318-343. [Google Scholar] [CrossRef] 

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