! 	  From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
! 		by RH Landau, MJ Paez, and CC Bordeianu 
! 		Copyright Wiley - VCH, 2007.
! 		Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
! 		MJ Paez, Univ Antioquia, 2007; and CC Bordeianu, Univ Bucharest, 2007.
! 		Supported by the US National Science Foundation							
! 
!   bessel.f95: Computation spherical Bessel functions by recurrence

Program bessel   

  Implicit none                                             
  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
	open(6, File = 'bessel.dat', Status = 'Unknown') ! open output file
 	Do	x = xmin, xmax, step
		 t1 = Down(x, order, start)
		 t2 = up(x, order)
		 write (6, 50) x, t1, t2
	End Do
	Close(6)
	50 Format (f15.10, f15.10, f15.10) 
	Stop 'data saved in bessel.dat'
End Program bessel
                                 ! calculate using Downward recursion
Function Down(x, order, start)        
	Implicit none
	Integer :: k, order, start
	Real*8 :: Down, scale, x, j(100)
                                                ! the arbitrary start
	j(start + 1) = 1
	j(start) = 1
	Do	k = start, 2, - 1
		 j(k - 1) = ((2*k - 1.0)/x)*j(k) - j(k + 1)
	End Do
	                                    ! scale so that j(1) = sin(x)/x
	scale = (sin(x)/x)/j(1)                  
	Down = j(order + 1)*scale
	Return
End
 
                                   ! 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 k = 1, (order - 1)
		 thr = ((2*k + 1.0)/x)*two - one
		 one = two
		 two = thr
		End Do
	up = thr
	Return
End