A Recursion Backbone for Circular and Elliptic Clausen Hierarchies
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912949088550912 |
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| author | Nagai, Ken |
| author_facet | Nagai, Ken |
| contents | We introduce an elliptic extension of Clausen-type functions based on a unified recursive framework. Starting from the polylogarithmic master function, we construct a pair of circular functions whose real and imaginary parts correspond to the classical Clausen-type structures. Replacing the trigonometric seed with a Jacobi theta function yields an elliptic deformation that preserves the same recursive backbone. The circular limit recovers the original functions, establishing a structural correspondence between the circular and elliptic settings. Furthermore, we introduce a generating deformation that organizes the recursion into a single analytic object. This viewpoint suggests a unified framework for Clausen-type functions and their elliptic analogues. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_06701 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Recursion Backbone for Circular and Elliptic Clausen Hierarchies Nagai, Ken General Mathematics 11M35 (Primary) 33E05, 33B30 (Secondary) We introduce an elliptic extension of Clausen-type functions based on a unified recursive framework. Starting from the polylogarithmic master function, we construct a pair of circular functions whose real and imaginary parts correspond to the classical Clausen-type structures. Replacing the trigonometric seed with a Jacobi theta function yields an elliptic deformation that preserves the same recursive backbone. The circular limit recovers the original functions, establishing a structural correspondence between the circular and elliptic settings. Furthermore, we introduce a generating deformation that organizes the recursion into a single analytic object. This viewpoint suggests a unified framework for Clausen-type functions and their elliptic analogues. |
| title | A Recursion Backbone for Circular and Elliptic Clausen Hierarchies |
| topic | General Mathematics 11M35 (Primary) 33E05, 33B30 (Secondary) |
| url | https://arxiv.org/abs/2603.06701 |