A unified framework for asymptotic analysis and computation of finite Hankel transform
Provides new computational tools for problems involving finite Hankel transforms, which are relevant in applied mathematics and engineering.
The paper develops a unified framework for asymptotic analysis and computation of the finite Hankel transform, enabling efficient numerical methods with asymptotic error estimates. Numerical examples validate the approach.
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.