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      FUNCTION PLM(L,M,X)
C LEGENDRE FUNCTIONS FOR (0.ge.L.le.8)
      IF(L.GT.0)GO TO 100
C L=0
      PLM=0.7071068
      RETURN
100   Y=X*X
      GO TO (1,2,3,4,5,6,7,8),L
C L=1
1     GO TO (10,11) M+1
10    PLM=1.2247449*X
      RETURN
11    PLM=0.8660254*(1.-Y)**0.5
      RETURN
C L=2
2     GO TO (20,21,22) M+1      
20    PLM=0.7905694*(-1.+3.*Y)
      RETURN
21    PLM=1.9364917*X*(1.-Y)**0.5
      RETURN
22    PLM=0.9682458*(1.-Y)
      RETURN
C L=3
3     GO TO (30,31,32,33) M+1
30    PLM=0.9354143*X*(-3.+5.*Y)
      RETURN
31    PLM=0.8100926*(1.-Y)**0.5*(-1.+5.*Y)
      RETURN
32    PLM=2.5617377*X*(1.-Y)
      RETURN
33    PLM=1.0458250*(1.-Y)**1.5
      RETURN
C L=4
4     GO TO (40,41,42,43,44) M+1
40    PLM=0.2651650*(3.+Y*(-30.+35.*Y))
      RETURN
41    PLM=1.1858541*X*(1.-Y)**0.5*(-3.+7.*Y)
      RETURN
42    PLM=0.8385255*(1.-Y)*(-1.+7.*Y)
      RETURN
43    PLM=3.1374751*X*(1.-Y)**1.5
      RETURN
44    PLM=1.1092650*(1.-Y)**2
      RETURN
C L=5
5     GO TO (50,51,52,53,54,55) M+1
50    PLM=0.2931510*X*(15.+Y*(-70.+63.*Y))
      RETURN
51    PLM=0.8028270*(1.-Y)**0.5*(1.+Y*(-14.+21.*Y))
      RETURN
52    PLM=4.2481614*X*(1.-Y)*(-1.+3.*Y)
      RETURN
53    PLM=0.8671523*(1.-Y)**1.5*(-1.+9.*Y)
      RETURN
54    PLM=3.6790157*X*(1.-Y)**2
      RETURN
55    PLM=1.1634069*(1.-Y)**2.5
      RETURN
C L=6
6     GO TO (60,61,62,63,64,65,66) M+1
60    PLM=0.15934436*(-5.+Y*(105.+Y*(-315.+231.*Y)))
      RETURN
61    PLM=1.0326695*X*(1.-Y)**0.5*(5.+Y*(-30.+33.*Y))
      RETURN
62    PLM=0.8163969*(1.-Y)*(1.+Y*(-18.+33.*Y))
      RETURN
63    PLM=1.6327938*X*(1.-Y)**1.5*(-3.+11.*Y)
      RETURN
64    PLM=0.8943180*(1.-Y)**2*(-1.+11.*Y)
      RETURN
65    PLM=4.1947232*X*(1.-Y)**2.5
      RETURN
66    PLM=1.2109123*(1.-Y)**3
      RETURN
C L=7
7     GO TO (70,71,72,73,74,75,76,77) M+1
70    PLM=0.1711633*X*(-35.+Y*(315.+Y*(-693.+429*Y)))
      RETURN
71    PLM=0.1601086*(1.-Y)**0.5*(-5.+Y*(135.+Y*(-495.+429*Y)))
      RETURN
72    PLM=0.3921844*X*(1.-Y)*(15.+Y*(-110.+143.*Y))
      RETURN
73    PLM=0.2773162*(1-Y)**1.5*(3.+Y*(-66.+143.*Y))
      RETURN
74    PLM=1.8395078*X*(1.-Y)**2*(-3.+13.*Y)
      RETURN
75    PLM=0.9197539*(1.-Y)**2.5*(-1.+13.*Y)
      RETURN
76    PLM=4.6898432*X*(1.-Y)**3
      RETURN
77    PLM=1.2534133*(1.-Y)**3.5
      RETURN
C L=8
8     GO TO (80,81,82,83,84,85,86,87,88) M+1
80    PLM=0.022777156*(35.+Y*(-1260.+Y*(6930.+Y*(-12012.+6435.*Y))))
      RETURN
81    PLM=0.1932706*X*(1.-Y)**0.5*(-35.+Y*(385.+Y*(-1001.+715.*Y)))
      RETURN
82    PLM=0.8085088*(1.-Y)*(-1.+Y*(33.+Y*(-143.+143.*Y)))
      RETURN
83    PLM=2.1894523*X*(1.-Y)**1.5*(3.+Y*(-26.+39.*Y))
      RETURN
84    plm=0.8479712*(1.-y)**2*(1.+y*(-26.+65.*y))
      RETURN
85    PLM=6.1148074*X*(1.-Y)**2.5*(-1.+5.*Y)
      RETURN
86    PLM=0.9435353*(1.-Y)**3*(-1.+15.*Y)
      RETURN
87    PLM=5.1679555*X*(1.-Y)**3.5
      RETURN
88    PLM=1.2919889*(1.-Y)**4
      RETURN
      END
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