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Journal of Applied Mathematics
Volume 2014, Article ID 105469, 7 pages
Research Article

Fast Hankel Transforms Algorithm Based on Kernel Function Interpolation with Exponential Functions

The State Key Laboratory of Transmission Equipment and System Safety and Electrical New Technology, Chongqing 400044, China

Received 24 December 2013; Revised 24 March 2014; Accepted 25 March 2014; Published 5 May 2014

Academic Editor: Laurent Gosse

Copyright © 2014 Huaiqing Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Pravin method for Hankel transforms is based on the decomposition of kernel function with exponential function. The defect of such method is the difficulty in its parameters determination and lack of adaptability to kernel function especially using monotonically decreasing functions to approximate the convex ones. This thesis proposed an improved scheme by adding new base function in interpolation procedure. The improved method maintains the merit of Pravin method which can convert the Hankel integral to algebraic calculation. The simulation results reveal that the improved method has high precision, high efficiency, and good adaptability to kernel function. It can be applied to zero-order and first-order Hankel transforms.