FUNCTION XK2DOP(TAU)
C     ====================
C
C     KERNEL FUNCTION K2 
C     AFTER  HUMMER,  1981, J.Q.S.R.T. 26, 187
C
      INCLUDE 'IMPLIC.FOR'
      PARAMETER (PI2SQ=2.506628275D0, PISQ=1.772453851D0, UN=1.D0,
     *   A1= -1.117897000D-1,   A2= -1.249099917D-1, 
     *   A3= -9.136358767D-3,   A4= -3.370280896D-4,
     *   B1=  1.566124168D-1,   B2=  9.013261660D-3,   
     *   B3=  1.908481163D-4,   B4= -1.547417750D-7, 
     *   B5= -6.657439727D-9,
     *   C1=  1.915049608D01,   C2=  1.007986843D02,   
     *   C3=  1.295307533D02,   C4= -3.143372468D01,
     *   D1=  1.968910391D01,   D2=  1.102576321D02,   
     *   D3=  1.694911399D02,   D4= -1.669969409D01,  
     *   D5= -3.666448000D01)
      XK2DOP=UN
      IF(TAU.LE.0.) RETURN
      IF(TAU.LE.11.) THEN
         P=UN+TAU*(A1+TAU*(A2+TAU*(A3+TAU*A4)))
         Q=UN+TAU*(B1+TAU*(B2+TAU*(B3+TAU*(B4+TAU*B5))))
         XK2DOP=TAU/PI2SQ*LOG(TAU/PISQ)+P/Q
       ELSE
         X=UN/LOG(TAU/PISQ)
         P=UN+X*(C1+X*(C2+X*(C3+X*C4)))
         Q=UN+X*(D1+X*(D2+X*(D3+X*(D4+X*D5))))
         XK2DOP=P/Q/2.D0/TAU/SQRT(LOG(TAU/PISQ))
      END IF
      RETURN
      END