Derivative polynomials and infinite series for squigonometric functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910892796411904 |
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| author | van Lith, Bart S. |
| author_facet | van Lith, Bart S. |
| contents | All squigonometric functions admit derivatives that can be expressed as polynomials of the squine and cosquine. We introduce a general framework that allows us to determine these polynomials recursively. We also provide an explicit formula for all coefficients of these polynomials. This also allows us to provide an explicit expression for the MacLaurin series coefficients of all squigonometric functions. We further discuss some methods that can compute the squigonometric functions up to any given tolerance over all of the real line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19624 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derivative polynomials and infinite series for squigonometric functions van Lith, Bart S. Classical Analysis and ODEs Numerical Analysis 26A06, 26A24 All squigonometric functions admit derivatives that can be expressed as polynomials of the squine and cosquine. We introduce a general framework that allows us to determine these polynomials recursively. We also provide an explicit formula for all coefficients of these polynomials. This also allows us to provide an explicit expression for the MacLaurin series coefficients of all squigonometric functions. We further discuss some methods that can compute the squigonometric functions up to any given tolerance over all of the real line. |
| title | Derivative polynomials and infinite series for squigonometric functions |
| topic | Classical Analysis and ODEs Numerical Analysis 26A06, 26A24 |
| url | https://arxiv.org/abs/2503.19624 |