On Somos’s theta-function identities of level 14. (English) Zbl 1412.11070
Summary: M. Somos discovered around 6200 theta-function identities of different levels using the computer and offered no proof for them. The purpose of this paper is to prove twenty four of his identities of level 14.
MSC:
| 11F20 | Dedekind eta function, Dedekind sums |
| 33C05 | Classical hypergeometric functions, \({}_2F_1\) |
References:
| [1] | Berndt, B.C.: Ramanujan’s Notebooks, Part III. Springer, New York (1991) · Zbl 0733.11001 · doi:10.1007/978-1-4612-0965-2 |
| [2] | Berndt, B.C.: Ramanujan’s Notebooks, Part IV. Springer, New York (1994) · Zbl 0785.11001 · doi:10.1007/978-1-4612-0879-2 |
| [3] | Ramanujan, S.: Notebooks (2 Volumes). Tata Institute of Fundamental Research, Bombay (1957) · Zbl 0138.24201 |
| [4] | Ramanujan, S.: The Lost Notebook and Other Unpublished Papers. Narosa, New Delhi (1988) · Zbl 0639.01023 |
| [5] | Somos, M.: Personal Communication |
| [6] | Yuttanan, B.: New modular equations in the spirit of Ramanujan. Ramanujan J. 29, 257-272 (2012) · Zbl 1285.11032 · doi:10.1007/s11139-012-9399-1 |
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