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Fast Hankel Transform Algorithm

The MATLAB routines in this directory implement Hankel transforms of order
0 and 1 by digital filtering.  These routines are based on a Fortran program
by Walt Anderson which was published as: 
 
  Anderson, W. L., 1979, Computer Program Numerical Integration of Related
  Hankel Transforms of Orders 0 and 1 by Adaptive Digital Filtering.
  Geophysic, 44(7):1287-1305.

The actual weights used in this code are from a later updated version
of the code that was originally published in 1979.

This digital filtering approach is appropriate for use only with functions
that are smooth.  If there are discontinuities in the function or its
derivatives then the code is likely to produce inaccurate results.  

For purposes of this code, the Hankel transforms are defined as
 
H0(B)=int(g(r)*J0(B*r),r=0..infinity)

and

H1(B)=int(g(r)*J1(B*r),r=0..infinity)
 
The routine hankel0 computes a 0th order transform.  The routine hankel1
computes a 1st order transform.  The routine hankel01 computes both 
transforms.  The test script does transforms on five functions with
known transforms and compares the results with known exact values.  
The functions c1 through c5 are the five functions that are transformed
by test.  
 
In some cases it can be helpful to compute several related functions
together and then apply the weights to do the transform.  The 
functions hankelpts and hankelwts can be used to do this.