On Ramanujan's $q$-Continued Fractions of Order Thirty-Four and Sixty-Eight
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911725321715712 |
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| author | Sarkar, Dipika Fathima, S. N. |
| author_facet | Sarkar, Dipika Fathima, S. N. |
| contents | We derived $q$-continued fractions $X_i(q)$ of order thirty-four and continued fractions $Y_i(q)$ of order sixty-eight from a general continued fraction identity of Ramanujan, where $i=1,2,3,4,5,6,7$ and $8$. We established some theta-function identities, and one has been proved for the continued fractions $X_i(q)$ and $Y_i(q)$. Furthermore, we obtained results on vanishing coefficients arising from these continued fractions and their reciprocals. As an application of the theta-function identities for $Y_i(q)$, we derived certain color partition identities. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_28841 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Ramanujan's $q$-Continued Fractions of Order Thirty-Four and Sixty-Eight Sarkar, Dipika Fathima, S. N. Number Theory 05A17, 11P83 We derived $q$-continued fractions $X_i(q)$ of order thirty-four and continued fractions $Y_i(q)$ of order sixty-eight from a general continued fraction identity of Ramanujan, where $i=1,2,3,4,5,6,7$ and $8$. We established some theta-function identities, and one has been proved for the continued fractions $X_i(q)$ and $Y_i(q)$. Furthermore, we obtained results on vanishing coefficients arising from these continued fractions and their reciprocals. As an application of the theta-function identities for $Y_i(q)$, we derived certain color partition identities. |
| title | On Ramanujan's $q$-Continued Fractions of Order Thirty-Four and Sixty-Eight |
| topic | Number Theory 05A17, 11P83 |
| url | https://arxiv.org/abs/2605.28841 |