FUNCTION bessk1(x)
      REAL bessk1,x
CU    USES bessi1
      REAL bessi1
      DOUBLE PRECISION p1,p2,p3,p4,p5,p6,p7,q1,q2,q3,q4,q5,q6,q7,y
      SAVE p1,p2,p3,p4,p5,p6,p7,q1,q2,q3,q4,q5,q6,q7
      DATA p1,p2,p3,p4,p5,p6,p7/1.0d0,0.15443144d0,-0.67278579d0,
     *-0.18156897d0,-0.1919402d-1,-0.110404d-2,-0.4686d-4/
      DATA q1,q2,q3,q4,q5,q6,q7/1.25331414d0,0.23498619d0,-0.3655620d-1,
     *0.1504268d-1,-0.780353d-2,0.325614d-2,-0.68245d-3/
      if (x.le.2.0) then
        y=x*x/4.0
        bessk1=(log(x/2.0)*bessi1(x))+(1.0/x)*(p1+y*(p2+y*(p3+y*(p4+y*
     *(p5+y*(p6+y*p7))))))
      else
        y=2.0/x
        bessk1=(exp(-x)/sqrt(x))*(q1+y*(q2+y*(q3+y*(q4+y*(q5+y*(q6+y*
     *q7))))))
      endif
      return
      END
C  (C) Copr. 1986-92 Numerical Recipes Software .