Using integral transforms to estimate higher order derivatives

TL;DR

This paper introduces a method using integral transforms to estimate high order derivatives of special functions, aiding in numerical integration error bounds by deriving integral representations and differentiating under the integral sign.

Contribution

It presents a novel approach employing integral transforms for high order derivative estimation, enhancing numerical integration accuracy.

Findings

Effective estimation of high order derivatives for special functions.

Improved error bounds in numerical integration.

Generalizable method for various functions.

Abstract

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.