function besin(n,x,factor,big)
    use fvn_common
    implicit none
    ! This function compute the rank n Bessel J function
    ! using recurrence relation :
    ! In+1(x)=-2n/x * In(x) + In-1(x)
    !
    ! Two optional parameters :
    ! factor : an integer that is used in Miller's algorithm to determine the
    ! starting point of iteration. Default value is 40, an increase of this value
    ! will increase accuracy. Starting point ~ nearest even integer of sqrt(factor*n)
    ! big : a real that determine the threshold for taking anti overflow counter measure
    ! default value is 1e10
    !
    real(sp_kind) :: besin
    integer :: n
    real(sp_kind) :: x
    integer, optional :: factor
    real(sp_kind), optional :: big

    integer :: tfactor
    real(sp_kind) :: tbig,tsmall
    real(sp_kind) :: two_on_x,binm1,bin,binp1,absx
    integer :: i,start
    real(sp_kind), external :: besi0,besi1

    ! Initialization of optional parameters
    tfactor=40
    if(present(factor)) tfactor=factor
    tbig=1e10
    if(present(big)) tbig=big
    tsmall=1./tbig

    if (n==0) then
        besin=besi0(x)
        return
    end if
    if (n==1) then
        besin=besi1(x)
        return
    end if
    if (n < 0) then
        write(*,*) "Error in besin, n must be >= 0"
        stop
    end if

    absx=abs(x)
    if (absx == 0.) then
        besin=0.
    else
        ! We use Miller's Algorithm
        ! as upward reccurence is unstable.
        ! This is adapted from Numerical Recipes
        ! Principle : use of downward recurrence from an arbitrary
        ! higher than n value with an arbitrary seed,
        ! and then use the normalization formula :
        ! 1=I0-2I2+2I4-2I6+.... however it is easier to use a
        ! call to besi0
        two_on_x=2./absx
        start=2*((n+int(sqrt(real(n*tfactor,sp_kind))))/2) ! even start
        binp1=0.
        bin=1.
        do i=start,1,-1
            ! begin downward rec
            binm1=two_on_x*bin*i+binp1
            binp1=bin
            bin=binm1
            ! Action to prevent overflow
            if (abs(bin) > tbig) then
                bin=bin*tsmall
                binp1=binp1*tsmall
                besin=besin*tsmall
            end if
            if (i==n) besin=binp1
        end do
        besin=besin*besi0(x)/bin
    end if
    ! if n is odd and x <0
    if ((x<0.) .and. (mod(n,2)==1)) besin=-besin

end function