Estimates of the Remainder in Taylor's Theorem Using the Henstock-Kurzweil Integral
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Abstract
When a real-valued function of one variable is approximated by its nth degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue p-norms in cases where f (n) or f (n+1) are Henstock-Kurzweil integrable. When the only assumption is that f (n) is Henstock-Kurzweil integrable then a modified form of the nth degree Taylor polynomial is used. When the only assumption is that f (n) ∈ C 0 then the remainder is estimated by applying the Alexiewicz norm to Schwartz distributions of order 1.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
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| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
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| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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