Continuous-Order Integral Operator for Function Reconstruction
Analysis
This paper introduces a novel continuous-order integral operator as an alternative to the Maclaurin expansion for reconstructing analytic functions. The core idea is to replace the discrete sum of derivatives with an integral over fractional derivative orders. The paper's significance lies in its potential to generalize the classical Taylor-Maclaurin expansion and provide a new perspective on function reconstruction. The use of fractional derivatives and the exploration of correction terms are key contributions.
Key Takeaways
- •Introduces a continuous-order integral operator for function reconstruction.
- •Replaces discrete sums of derivatives with an integral over fractional derivative orders.
- •Demonstrates accurate reconstruction with low-order correction terms.
- •Offers a framework for generalizing the Taylor-Maclaurin expansion.
Reference
“The operator reconstructs f accurately in the tested domains.”