17 October   2014   8:39:03.857 PM      
 
LEGENDRE_POLYNOMIAL_PRB:
  FORTRAN77 version.
  Test the LEGENDRE_POLYNOMIAL library.
 
LEGENDRE_POLYNOMIAL_TEST01:
  P_POLYNOMIAL_VALUES stores values of
  the Legendre polynomial P(n,x).
  P_POLYNOMIAL_VALUE evaluates.
 
                        Tabulated                 Computed
     N        X           P(N,X)                    P(N,X)                     Error
 
     0      0.250000     1.000000000000000         1.000000000000000       0.0    
     1      0.250000    0.2500000000000000        0.2500000000000000       0.0    
     2      0.250000   -0.4062500000000000       -0.4062500000000000       0.0    
     3      0.250000   -0.3359375000000000       -0.3359375000000000       0.0    
     4      0.250000    0.1577148437500000        0.1577148437500000       0.0    
     5      0.250000    0.3397216796875000        0.3397216796875000       0.0    
     6      0.250000    0.2427673339843750E-01    0.2427673339843750E-01   0.0    
     7      0.250000   -0.2799186706542969       -0.2799186706542969       0.0    
     8      0.250000   -0.1524540185928345       -0.1524540185928345      -.28E-16
     9      0.250000    0.1768244206905365        0.1768244206905365       0.0    
    10      0.250000    0.2212002165615559        0.2212002165615559      0.28E-16
     3      0.000000     0.000000000000000        -0.000000000000000       0.0    
     3      0.100000   -0.1475000000000000       -0.1475000000000000       0.0    
     3      0.200000   -0.2800000000000000       -0.2800000000000000       0.0    
     3      0.300000   -0.3825000000000000       -0.3825000000000000       0.0    
     3      0.400000   -0.4400000000000000       -0.4399999999999999      -.56E-16
     3      0.500000   -0.4375000000000000       -0.4375000000000000       0.0    
     3      0.600000   -0.3600000000000000       -0.3600000000000000      0.56E-16
     3      0.700000   -0.1925000000000000       -0.1925000000000001      0.11E-15
     3      0.800000    0.8000000000000000E-01    0.8000000000000022E-01  -.22E-15
     3      0.900000    0.4725000000000000        0.4725000000000001      -.11E-15
     3      1.000000     1.000000000000000         1.000000000000000       0.0    
 
LEGENDRE_POLYNOMIAL_TEST015:
  P_POLYNOMIAL_PRIME evaluates the derivative
  of the Legendre polynomial.
 
                        Computed
     N        X           P'(N,X)
 
 
     0     -1.000000     0.000000000000000    
     1     -1.000000     1.000000000000000    
     2     -1.000000    -3.000000000000000    
     3     -1.000000     6.000000000000000    
     4     -1.000000    -10.00000000000000    
     5     -1.000000     15.00000000000000    
 
     0     -0.800000     0.000000000000000    
     1     -0.800000     1.000000000000000    
     2     -0.800000    -2.400000000000000    
     3     -0.800000     3.300000000000001    
     4     -0.800000    -2.960000000000001    
     5     -0.800000     1.203000000000002    
 
     0     -0.600000     0.000000000000000    
     1     -0.600000     1.000000000000000    
     2     -0.600000    -1.800000000000000    
     3     -0.600000     1.199999999999999    
     4     -0.600000    0.7200000000000008    
     5     -0.600000    -2.472000000000000    
 
     0     -0.400000     0.000000000000000    
     1     -0.400000     1.000000000000000    
     2     -0.400000    -1.200000000000000    
     3     -0.400000   -0.2999999999999998    
     4     -0.400000     1.880000000000000    
     5     -0.400000    -1.317000000000000    
 
     0     -0.200000     0.000000000000000    
     1     -0.200000     1.000000000000000    
     2     -0.200000   -0.6000000000000001    
     3     -0.200000    -1.200000000000000    
     4     -0.200000     1.360000000000000    
     5     -0.200000    0.8879999999999999    
 
     0      0.000000     0.000000000000000    
     1      0.000000     1.000000000000000    
     2      0.000000     0.000000000000000    
     3      0.000000    -1.500000000000000    
     4      0.000000    -0.000000000000000    
     5      0.000000     1.875000000000000    
 
     0      0.200000     0.000000000000000    
     1      0.200000     1.000000000000000    
     2      0.200000    0.6000000000000001    
     3      0.200000    -1.200000000000000    
     4      0.200000    -1.360000000000000    
     5      0.200000    0.8879999999999999    
 
     0      0.400000     0.000000000000000    
     1      0.400000     1.000000000000000    
     2      0.400000     1.200000000000000    
     3      0.400000   -0.2999999999999998    
     4      0.400000    -1.880000000000000    
     5      0.400000    -1.317000000000000    
 
     0      0.600000     0.000000000000000    
     1      0.600000     1.000000000000000    
     2      0.600000     1.800000000000000    
     3      0.600000     1.199999999999999    
     4      0.600000   -0.7200000000000008    
     5      0.600000    -2.472000000000000    
 
     0      0.800000     0.000000000000000    
     1      0.800000     1.000000000000000    
     2      0.800000     2.400000000000000    
     3      0.800000     3.300000000000001    
     4      0.800000     2.960000000000001    
     5      0.800000     1.203000000000002    
 
     0      1.000000     0.000000000000000    
     1      1.000000     1.000000000000000    
     2      1.000000     3.000000000000000    
     3      1.000000     6.000000000000000    
     4      1.000000     10.00000000000000    
     5      1.000000     15.00000000000000    
 
LEGENDRE_POLYNOMIAL_TEST016:
  P_POLYNOMIAL_PRIME2 evaluates the second
  derivative of the Legendre polynomial.
 
                        Computed
     N        X           P"(N,X)
 
 
     0     -1.000000     0.000000000000000    
     1     -1.000000     0.000000000000000    
     2     -1.000000     3.000000000000000    
     3     -1.000000    -15.00000000000000    
     4     -1.000000     45.00000000000000    
     5     -1.000000    -105.0000000000000    
 
     0     -0.800000     0.000000000000000    
     1     -0.800000     0.000000000000000    
     2     -0.800000     3.000000000000000    
     3     -0.800000    -12.00000000000000    
     4     -0.800000     26.10000000000000    
     5     -0.800000    -38.64000000000001    
 
     0     -0.600000     0.000000000000000    
     1     -0.600000     0.000000000000000    
     2     -0.600000     3.000000000000000    
     3     -0.600000    -8.999999999999998    
     4     -0.600000     11.40000000000000    
     5     -0.600000    -2.519999999999995    
 
     0     -0.400000     0.000000000000000    
     1     -0.400000     0.000000000000000    
     2     -0.400000     3.000000000000000    
     3     -0.400000    -6.000000000000001    
     4     -0.400000    0.9000000000000012    
     5     -0.400000     10.92000000000000    
 
     0     -0.200000     0.000000000000000    
     1     -0.200000     0.000000000000000    
     2     -0.200000     3.000000000000000    
     3     -0.200000    -3.000000000000000    
     4     -0.200000    -5.399999999999999    
     5     -0.200000     9.239999999999998    
 
     0      0.000000     0.000000000000000    
     1      0.000000     0.000000000000000    
     2      0.000000     3.000000000000000    
     3      0.000000     0.000000000000000    
     4      0.000000    -7.500000000000000    
     5      0.000000    -0.000000000000000    
 
     0      0.200000     0.000000000000000    
     1      0.200000     0.000000000000000    
     2      0.200000     3.000000000000000    
     3      0.200000     3.000000000000000    
     4      0.200000    -5.399999999999999    
     5      0.200000    -9.239999999999998    
 
     0      0.400000     0.000000000000000    
     1      0.400000     0.000000000000000    
     2      0.400000     3.000000000000000    
     3      0.400000     6.000000000000001    
     4      0.400000    0.9000000000000012    
     5      0.400000    -10.92000000000000    
 
     0      0.600000     0.000000000000000    
     1      0.600000     0.000000000000000    
     2      0.600000     3.000000000000000    
     3      0.600000     8.999999999999998    
     4      0.600000     11.40000000000000    
     5      0.600000     2.519999999999995    
 
     0      0.800000     0.000000000000000    
     1      0.800000     0.000000000000000    
     2      0.800000     3.000000000000000    
     3      0.800000     12.00000000000000    
     4      0.800000     26.10000000000000    
     5      0.800000     38.64000000000001    
 
     0      1.000000     0.000000000000000    
     1      1.000000     0.000000000000000    
     2      1.000000     3.000000000000000    
     3      1.000000     15.00000000000000    
     4      1.000000     45.00000000000000    
     5      1.000000     105.0000000000000    
 
LEGENDRE_POLYNOMIAL_TEST02
  P_POLYNOMIAL_COEFFICIENTS determines polynomial coefficients of P(n,x).
 
  P( 0,x) = 
 
     1.00000    
 
  P( 1,x) = 
 
     1.00000     * x
 
  P( 2,x) = 
 
     1.50000     * x^ 2
   -0.500000    
 
  P( 3,x) = 
 
     2.50000     * x^ 3
    -1.50000     * x
 
  P( 4,x) = 
 
     4.37500     * x^ 4
    -3.75000     * x^ 2
    0.375000    
 
  P( 5,x) = 
 
     7.87500     * x^ 5
    -8.75000     * x^ 3
     1.87500     * x
 
  P( 6,x) = 
 
     14.4375     * x^ 6
    -19.6875     * x^ 4
     6.56250     * x^ 2
   -0.312500    
 
  P( 7,x) = 
 
     26.8125     * x^ 7
    -43.3125     * x^ 5
     19.6875     * x^ 3
    -2.18750     * x
 
  P( 8,x) = 
 
     50.2734     * x^ 8
    -93.8438     * x^ 6
     54.1406     * x^ 4
    -9.84375     * x^ 2
    0.273438    
 
  P( 9,x) = 
 
     94.9609     * x^ 9
    -201.094     * x^ 7
     140.766     * x^ 5
    -36.0938     * x^ 3
     2.46094     * x
 
  P(10,x) = 
 
     180.426     * x^10
    -427.324     * x^ 8
     351.914     * x^ 6
    -117.305     * x^ 4
     13.5352     * x^ 2
   -0.246094    
 
LEGENDRE_POLYNOMIAL_TEST03:
  P_POLYNOMIAL_ZEROS computes the zeros of P(n,x)
  Check by calling P_POLYNOMIAL_VALUE.
 
  Computed zeros for P(1,z):
 
         1:    0.0000000    
 
  Evaluate P(1,z):
 
         1:    0.0000000    
 
  Computed zeros for P(2,z):
 
         1:  -0.57735027    
         2:   0.57735027    
 
  Evaluate P(2,z):
 
         1:    0.0000000    
         2:    0.0000000    
 
  Computed zeros for P(3,z):
 
         1:  -0.77459667    
         2:   0.19949320E-16
         3:   0.77459667    
 
  Evaluate P(3,z):
 
         1:    0.0000000    
         2:    0.0000000    
         3:    0.0000000    
 
  Computed zeros for P(4,z):
 
         1:  -0.86113631    
         2:  -0.33998104    
         3:   0.33998104    
         4:   0.86113631    
 
  Evaluate P(4,z):
 
         1:    0.0000000    
         2:    0.0000000    
         3:    0.0000000    
         4:    0.0000000    
 
  Computed zeros for P(5,z):
 
         1:  -0.90617985    
         2:  -0.53846931    
         3:  -0.10818539E-15
         4:   0.53846931    
         5:   0.90617985    
 
  Evaluate P(5,z):
 
         1:  -0.97699626E-15
         2:  -0.31086245E-15
         3:  -0.20284760E-15
         4:  -0.44408921E-16
         5:  -0.10658141E-14
 
LEGENDRE_POLYNOMIAL_TEST04:
  P_QUADRATURE_RULE computes the quadrature
  rule associated with P(n,x)
 
      X            W
 
         1:  -0.906180        0.236927    
         2:  -0.538469        0.478629    
         3:  -0.108185E-15    0.568889    
         4:   0.538469        0.478629    
         5:   0.906180        0.236927    
 
  Use the quadrature rule to estimate:
 
    Q = Integral ( -1 <= X < +1 ) X^E dx
 
   E       Q_Estimate      Q_Exact
 
   0     2.00000         2.00000    
   1    0.277556E-16     0.00000    
   2    0.666667        0.666667    
   3   -0.138778E-15     0.00000    
   4    0.400000        0.400000    
   5   -0.222045E-15     0.00000    
   6    0.285714        0.285714    
   7   -0.249800E-15     0.00000    
   8    0.222222        0.222222    
   9   -0.249800E-15     0.00000    
 
LEGENDRE_POLYNOMIAL_TEST05
  Compute an exponential product table for P(n,x):
 
  Tij = integral ( -1 <= x <= +1 ) exp(b*x) P(i,x) P(j,x) dx
 
  Maximum degree P =      5
  Exponential argument coefficient B =    0.00000    
 
  Exponential product table:
 
  Col         1             2             3             4             5       
  Row
 
    1:   2.00000      0.333067E-15  0.735523E-15  0.180411E-15 -0.791034E-15
    2:  0.333067E-15  0.666667      0.208167E-15 -0.124900E-15 -0.818789E-15
    3:  0.735523E-15  0.208167E-15  0.400000     -0.645317E-15 -0.971445E-16
    4:  0.180411E-15 -0.124900E-15 -0.638378E-15  0.285714     -0.222045E-15
    5: -0.791034E-15 -0.811851E-15 -0.124900E-15 -0.215106E-15  0.222222    
    6: -0.165146E-14 -0.513478E-15 -0.291434E-15 -0.381639E-15 -0.693889E-17
 
  Col         6       
  Row
 
    1: -0.165146E-14
    2: -0.506539E-15
    3: -0.291434E-15
    4: -0.374700E-15
    5: -0.693889E-17
    6:  0.181818    
 
LEGENDRE_POLYNOMIAL_TEST05
  Compute an exponential product table for P(n,x):
 
  Tij = integral ( -1 <= x <= +1 ) exp(b*x) P(i,x) P(j,x) dx
 
  Maximum degree P =      5
  Exponential argument coefficient B =    1.00000    
 
  Exponential product table:
 
  Col         1             2             3             4             5       
  Row
 
    1:   2.35040      0.735759      0.143126      0.201302E-01  0.221447E-02
    2:  0.735759      0.878885      0.306382      0.626050E-01  0.905782E-02
    3:  0.143126      0.306382      0.512112      0.194658      0.414752E-01
    4:  0.201302E-01  0.626050E-01  0.194658      0.363558      0.143849    
    5:  0.221447E-02  0.905782E-02  0.414752E-01  0.143849      0.282170    
    6:  0.199925E-03  0.101492E-02  0.615177E-02  0.313811E-01  0.114325    
 
  Col         6       
  Row
 
    1:  0.199925E-03
    2:  0.101492E-02
    3:  0.615177E-02
    4:  0.313811E-01
    5:  0.114325    
    6:  0.230635    
 
LEGENDRE_POLYNOMIAL_TEST06
  Compute a power product table for P(n,x):
 
  Tij = integral ( -1 <= x <= +1 ) x^e P(i,x) P(j,x) dx
 
  Maximum degree P =      5
  Exponent of X, E =              0
 
  Power product table:
 
  Col         1             2             3             4             5       
  Row
 
    1:   2.00000      0.305311E-15  0.971445E-15  0.138778E-15  0.568989E-15
    2:  0.305311E-15  0.666667      0.166533E-15  0.721645E-15  0.235922E-15
    3:  0.971445E-15  0.166533E-15  0.400000      0.235922E-15  0.360822E-15
    4:  0.138778E-15  0.749401E-15  0.222045E-15  0.285714      0.277556E-16
    5:  0.568989E-15  0.235922E-15  0.374700E-15  0.138778E-16  0.222222    
    6:  0.319189E-15  0.201228E-15   0.00000      0.267147E-15  0.433681E-16
 
  Col         6       
  Row
 
    1:  0.319189E-15
    2:  0.180411E-15
    3:  0.346945E-17
    4:  0.260209E-15
    5:  0.503070E-16
    6:  0.181818    
 
LEGENDRE_POLYNOMIAL_TEST06
  Compute a power product table for P(n,x):
 
  Tij = integral ( -1 <= x <= +1 ) x^e P(i,x) P(j,x) dx
 
  Maximum degree P =      5
  Exponent of X, E =              1
 
  Power product table:
 
  Col         1             2             3             4             5       
  Row
 
    1:  0.915934E-15  0.666667      0.208167E-15 -0.360822E-15 -0.346945E-15
    2:  0.666667      0.430211E-15  0.266667     -0.138778E-15 -0.374700E-15
    3:  0.208167E-15  0.266667      0.138778E-16  0.171429     -0.277556E-15
    4: -0.360822E-15 -0.138778E-15  0.171429     -0.166533E-15  0.126984    
    5: -0.346945E-15 -0.374700E-15 -0.263678E-15  0.126984     -0.138778E-16
    6: -0.395517E-15 -0.423273E-15 -0.326128E-15 -0.971445E-16  0.101010    
 
  Col         6       
  Row
 
    1: -0.395517E-15
    2: -0.437150E-15
    3: -0.326128E-15
    4: -0.104083E-15
    5:  0.101010    
    6:  0.277556E-16
 
LEGENDRE_POLYNOMIAL_TEST07:
  PM_POLYNOMIAL_VALUES stores values of
  the Legendre polynomial Pm(n,m,x).
  PM_POLYNOMIAL_VALUE evaluates.
 
                                Tabulated                 Computed
     N     M        X           Pm(N,M,X)                 Pm(N,M,X)             Error
 
     1     0      0.000000     0.000000000000000         0.000000000000000       0.0    
     2     0      0.000000   -0.5000000000000000       -0.5000000000000000       0.0    
     3     0      0.000000     0.000000000000000        -0.000000000000000       0.0    
     4     0      0.000000    0.3750000000000000        0.3750000000000000       0.0    
     5     0      0.000000     0.000000000000000         0.000000000000000       0.0    
     1     1      0.500000   -0.8660254037844386       -0.8660254037844386       0.0    
     2     1      0.500000    -1.299038105676658        -1.299038105676658       0.0    
     3     1      0.500000   -0.3247595264191645       -0.3247595264191645       0.0    
     4     1      0.500000     1.353164693413185         1.353164693413185      -.44E-15
     3     0      0.200000   -0.2800000000000000       -0.2800000000000000       0.0    
     3     1      0.200000     1.175755076535925         1.175755076535925      -.44E-15
     3     2      0.200000     2.880000000000000         2.880000000000000       0.0    
     3     3      0.200000    -14.10906091843111        -14.10906091843110      -.71E-14
     4     2      0.250000    -3.955078125000000        -3.955078125000000      0.44E-15
     5     2      0.250000    -9.997558593750000        -9.997558593750002      0.18E-14
     6     3      0.250000     82.65311444100485         82.65311444100486      -.14E-13
     7     3      0.250000     20.24442836815152         20.24442836815153      -.11E-13
     8     4      0.250000    -423.7997531890869        -423.7997531890869      -.57E-13
     9     4      0.250000     1638.320624828339         1638.320624828339       0.0    
    10     5      0.250000    -20256.87389227225        -20256.87389227226      0.36E-11
 
LEGENDRE_POLYNOMIAL_TEST08:
  PMN_POLYNOMIAL_VALUES stores values of
  the Legendre polynomial Pmn(n,m,x).
  PMN_POLYNOMIAL_VALUE evaluates.
 
                                Tabulated                 Computed
     N     M        X           Pmn(N,M,X)                Pmn(N,M,X)             Error
 
     0     0      0.500000    0.7071067811865475        0.7071067811865476      -.11E-15
     1     0      0.500000    0.6123724356957945        0.6123724356957945       0.0    
     1     1      0.500000   -0.7500000000000000       -0.7499999999999999      -.11E-15
     2     0      0.500000   -0.1976423537605237       -0.1976423537605237      0.28E-16
     2     1      0.500000   -0.8385254915624211       -0.8385254915624212      0.11E-15
     2     2      0.500000    0.7261843774138907        0.7261843774138906      0.11E-15
     3     0      0.500000   -0.8184875533567997       -0.8184875533567997       0.0    
     3     1      0.500000   -0.1753901900050285       -0.1753901900050285      0.28E-16
     3     2      0.500000    0.9606516343087123        0.9606516343087123       0.0    
     3     3      0.500000   -0.6792832849776299       -0.6792832849776300      0.11E-15
     4     0      0.500000   -0.6131941618102092       -0.6131941618102091      -.11E-15
     4     1      0.500000    0.6418623720763665        0.6418623720763665       0.0    
     4     2      0.500000    0.4716705890038619        0.4716705890038619       0.0    
     4     3      0.500000    -1.018924927466445        -1.018924927466445       0.0    
     4     4      0.500000    0.6239615396237876        0.6239615396237875      0.11E-15
     5     0      0.500000    0.2107022704608181        0.2107022704608181      -.28E-16
     5     1      0.500000    0.8256314721961969        0.8256314721961968      0.11E-15
     5     2      0.500000   -0.3982651281554632       -0.3982651281554632      -.56E-16
     5     3      0.500000   -0.7040399320721435       -0.7040399320721434      -.11E-15
     5     4      0.500000     1.034723155272289         1.034723155272289      0.44E-15
     5     5      0.500000   -0.5667412129155530       -0.5667412129155530       0.0    
 
LEGENDRE_POLYNOMIAL_TEST09:
  PMNS_POLYNOMIAL_VALUES stores values of
  the Legendre polynomial Pmns(n,m,x).
  PMNS_POLYNOMIAL_VALUE evaluates.
 
                                Tabulated                 Computed
     N     M        X           Pmns(N,M,X)                Pmns(N,M,X)             Error
 
     0     0      0.500000    0.2820947917738781        0.2820947917738781      -.56E-16
     1     0      0.500000    0.2443012559514600        0.2443012559514600      0.28E-16
     1     1      0.500000   -0.2992067103010745       -0.2992067103010745       0.0    
     2     0      0.500000   -0.7884789131313000E-01   -0.7884789131313001E-01  0.14E-16
     2     1      0.500000   -0.3345232717786446       -0.3345232717786445      -.56E-16
     2     2      0.500000    0.2897056515173922        0.2897056515173921      0.56E-16
     3     0      0.500000   -0.3265292910163510       -0.3265292910163510       0.0    
     3     1      0.500000   -0.6997056236064664E-01   -0.6997056236064664E-01   0.0    
     3     2      0.500000    0.3832445536624809        0.3832445536624809      -.56E-16
     3     3      0.500000   -0.2709948227475519       -0.2709948227475519      0.56E-16
     4     0      0.500000   -0.2446290772414100       -0.2446290772414100      -.28E-16
     4     1      0.500000    0.2560660384200185        0.2560660384200185       0.0    
     4     2      0.500000    0.1881693403754876        0.1881693403754876      0.28E-16
     4     3      0.500000   -0.4064922341213279       -0.4064922341213280      0.56E-16
     4     4      0.500000    0.2489246395003027        0.2489246395003027      -.56E-16
     5     0      0.500000    0.8405804426339820E-01    0.8405804426339822E-01  -.14E-16
     5     1      0.500000    0.3293793022891428        0.3293793022891428       0.0    
     5     2      0.500000   -0.1588847984307093       -0.1588847984307093      0.28E-16
     5     3      0.500000   -0.2808712959945307       -0.2808712959945307       0.0    
     5     4      0.500000    0.4127948151484925        0.4127948151484925       0.0    
     5     5      0.500000   -0.2260970318780046       -0.2260970318780046      0.28E-16
 
LEGENDRE_POLYNOMIAL_TEST095
  PN_POLYNOMIAL_COEFFICIENTS determines polynomial coefficients of Pn(n,x).
 
  P( 0,x) = 
 
    0.707107    
 
  P( 1,x) = 
 
     1.22474     * x
 
  P( 2,x) = 
 
     2.37171     * x^ 2
   -0.790569    
 
  P( 3,x) = 
 
     4.67707     * x^ 3
    -2.80624     * x
 
  P( 4,x) = 
 
     9.28078     * x^ 4
    -7.95495     * x^ 2
    0.795495    
 
  P( 5,x) = 
 
     18.4685     * x^ 5
    -20.5206     * x^ 3
     4.39726     * x
 
  P( 6,x) = 
 
     36.8085     * x^ 6
    -50.1935     * x^ 4
     16.7312     * x^ 2
   -0.796722    
 
  P( 7,x) = 
 
     73.4291     * x^ 7
    -118.616     * x^ 5
     53.9164     * x^ 3
    -5.99072     * x
 
  P( 8,x) = 
 
     146.571     * x^ 8
    -273.599     * x^ 6
     157.846     * x^ 4
    -28.6992     * x^ 2
    0.797200    
 
  P( 9,x) = 
 
     292.689     * x^ 9
    -619.813     * x^ 7
     433.869     * x^ 5
    -111.248     * x^ 3
     7.58512     * x
 
  P(10,x) = 
 
     584.646     * x^10
    -1384.69     * x^ 8
     1140.33     * x^ 6
    -380.111     * x^ 4
     43.8589     * x^ 2
   -0.797435    
 
LEGENDRE_POLYNOMIAL_TEST10
  Compute a pair product table for Pn(n,x):
 
  Tij = integral ( -1 <= x <= +1 ) Pn(i,x) Pn(j,x) dx
 
  The Pn(n,x) polynomials are orthonormal,
  so T should be the identity matrix.
 
  Maximum degree P =      5
 
  Pair product table:
 
  Col         1             2             3             4             5       
  Row
 
    1:   1.00000      0.277556E-15  0.999201E-15  0.166533E-15  0.874301E-15
    2:  0.249800E-15   1.00000      0.333067E-15  0.174860E-14  0.666134E-15
    3:  0.102696E-14  0.305311E-15   1.00000      0.666134E-15  0.119349E-14
    4:  0.194289E-15  0.169309E-14  0.777156E-15   1.00000      0.277556E-16
    5:  0.888178E-15  0.666134E-15  0.122125E-14  0.277556E-16   1.00000    
    6:  0.541234E-15  0.555112E-15   0.00000      0.116573E-14  0.194289E-15
 
  Col         6       
  Row
 
    1:  0.513478E-15
    2:  0.638378E-15
    3:  0.277556E-16
    4:  0.116573E-14
    5:  0.194289E-15
    6:   1.00000    
 
LEGENDRE_POLYNOMIAL_PRB:
  Normal end of execution.
 
17 October   2014   8:39:03.862 PM