P1 Function

  FUNCTION P1(g,p,k,l,x)
    IMPLICIT NONE
    REAL(rp) :: P1
    REAL(rp), INTENT(IN) ::	g
    REAL(rp), INTENT(IN) :: p
    REAL(rp), INTENT(IN) :: k
    REAL(rp), INTENT(IN) :: l
    REAL(rp), INTENT(IN) :: x
    REAL(rp) :: BK13
    REAL(rp) :: BK23
    REAL(rp) :: v
    REAL(rp) :: A

    v = 1.0_rp/3.0_rp
    BK13 = besselk(v,zeta(g,p,k,l))

    v = 2.0_rp/3.0_rp
    BK23 = besselk(v,zeta(g,p,k,l))

    A = fx(g,p,x)

    P1 = ((g*p)**2)*BK13*COS(arg(g,p,k,l,x))/(1.0_rp + (g*p)**2) - &
         0.5_rp*BK13*(1.0_rp + A**2)*COS(arg(g,p,k,l,x)) &
         + A*BK23*SIN(arg(g,p,k,l,x))
  END FUNCTION P1