c  From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
c  by RH Landau, MJ Paez, and CC Bordeianu 
c  Copyright Wiley-VCH, 2007.
c  Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
c  MJ Paez, Univ Antioquia, 2007; and CC Bordeianu, Univ Bucharest, 2007.
c  Support by National Science Foundation                              
c					
c  bessel.f:  Spherical Bessel functions via up and down recursion  
c             data saved as: x y1 y2  

      Program bessel
			
 	      Implicit none
c order of Bessel function, x range, stepsize, start for downward alg
	      Real*8 step, x, xmin, xmax, up, down, t1, t2
	      Integer order, start
	      xmin = 0.25
	      xmax = 40.0
	      step = 0.1
	      order = 10
	      start = 50
c                                                    open output file
	      Open(6, File = 'bessel.dat', Status = 'Unknown')
c                                                        main program
	      Do 10 x = xmin, xmax, step
	        t1 = down(x, order, start)
	        t2 = up(x, order)
	        Write (6, *) x, t1, t2
 10   	Continue
      	Close(6)
 	      Stop 'data saved in bessel.dat'
 	    End
c                                  calculate using downward recursion
	    Function down(x, order, start)
	      Implicit none
	      Integer k, order, start
	      Real*8 down, scale, x, j(100)
c                                                     arbitrary start
	      j(start+1) = 1
	      j(start) = 1
	      Do 20 k = start, 2, -1
	        j(k-1) = ((2*k-1.0)/x)*j(k)-j(k+1)
 20    	Continue
c                                       scale so that j(1) = sin(x)/x
        scale = (sin(x)/x)/j(1)
        down = j(order+1)*scale
        Return
      End
c                                    calculate using upward recursion
	    Function up(x, order)
	      Implicit none
	      Integer k, order
	      Real*8 up, x, one, two, thr
	      one = sin(x)/x
	      two = (sin(x)-x*cos(x))/(x*x)
	      Do 30 k = 1, (order-1)
	        thr = ((2*k+1.0)/x)*two-one
	        one = two
	        two = thr
 30	    Continue
 	      up = thr
 	      Return
 	    End