Using integral transforms to estimate higher order derivatives
Provides a theoretical tool for estimating derivatives in numerical analysis, but the contribution is incremental and lacks empirical validation.
The paper develops a method using integral transforms to estimate high-order derivatives of special functions, applied to numerical integration error bounds. No concrete numerical results are provided.
Integral transformations are used to estimate high order derivatives of various special functions. Applications are given to numerical integration, where estimates of high order derivatives of the integrand are needed to achieve bounds on the error. The main idea is to find a suitable integral representation of the function whose derivatives are to be estimated, differentiate repeatedly under the integral sign, and estimate the resulting integral.