A unified framework for asymptotic analysis and computation of finite Hankel transform

TL;DR

This paper introduces a unified framework for analyzing and computing the finite Hankel transform, providing asymptotic expansions and efficient numerical methods with error estimates, validated by numerical examples.

Contribution

It develops a comprehensive approach for asymptotic analysis and numerical computation of the finite Hankel transform, including cases with zeros and stationary points.

Findings

Derived asymptotic expansions for the finite Hankel transform.

Developed two efficient numerical methods with error analysis.

Validated methods through numerical experiments.

Abstract

In this paper we present a unified framework for asymptotic analysis and computation of the finite Hankel transform. This framework enables us to derive asymptotic expansions of the transform, including the cases where the oscillator has zeros and stationary points. As a consequence, two efficient and affordable methods for computing the transform numerically are developed and a detailed analysis of their asymptotic error estimate is carried out. Numerical examples are provided to confirm our analysis.