## File: zbesselb.f90

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elkcode 5.4.24-2
 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879  ! Copyright (C) 2008 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: zbesselb ! !INTERFACE: subroutine zbesselb(lmax,x,b) ! !INPUT/OUTPUT PARAMETERS: ! lmax : maximum order of Bessel function (in,integer) ! x : real argument (in,real) ! b : array of returned values (out,real(0:lmax)) ! !DESCRIPTION: ! Computes variations of the spherical Bessel function ! $b_l(x)=i^lh^{(1)}_l(ix)$, for real argument $x$ and ! $l=0,1,\ldots,l_{\rm max}$. The recursion relation ! $$j_{l+1}(x)=\frac{2l+1}{x}j_l(x)+j_{l-1}(x)$$ ! is used upwards. For starting values there are ! $$b_0(x)=-\frac{e^{-x}}{x};\qquad b_1(x)=b_0(x)\left\{1+\frac{1}{x} ! \right\}.$$ ! For $x\ll 1$ the asymtotic forms ! $$b_l(x)\approx\frac{-(2l-1)!!}{(-x)^{l+1}}$$ ! are used. ! ! !REVISION HISTORY: ! Created April 2008 from sbessel routine (Lars Nordstrom) !EOP !BOC implicit none ! arguments integer, intent(in) :: lmax real(8), intent(in) :: x real(8), intent(out) :: b(0:lmax) ! local variables integer l real(8) xi,b0,b1,bt,t3,t4 if ((lmax.lt.0).or.(lmax.gt.50)) then write(*,*) write(*,'("Error(zbesselb): lmax out of range : ",I8)') lmax write(*,*) stop end if if ((x.lt.0.d0).or.(x.gt.1.d8)) then write(*,*) write(*,'("Error(zbesselb): x out of range : ",G18.10)') x write(*,*) stop end if xi=1.d0/x ! treat x << 1 if (x.lt.1.d-7) then b(0)=-xi t3=-1.d0 t4=xi do l=1,lmax t3=t3*dble(2*l-1) t4=t4*xi b(l)=t4*t3 end do return end if ! recurse up b(0)=-xi*exp(-x) if (lmax.eq.0) return b(1)=b(0)*(1.d0+xi) if (lmax.eq.1) return b0=b(0) b1=b(1) do l=2,lmax bt=dble(2*l-1)*b1*xi+b0 b0=b1 b1=bt b(l)=b1 end do return end subroutine !EOC