amn.RdMatrix of coefficients of the Taylor series for \(\sigma(z)\) as described on page 636 and tabulated on page 637.
amn(u)Reproduces the coefficients \(a_{mn}\) on page 637 according to recurrence formulae 18.5.7 and 18.5.8, p636. Used in equation 18.5.6.
amn(12) #page 637
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1.000000e+00 -1.000000e+00 -9.000000e+00 6.900000e+01 3.210000e+02
#> [2,] -3.000000e+00 -1.800000e+01 5.130000e+02 3.358800e+04 2.808945e+06
#> [3,] -5.400000e+01 4.968000e+03 2.575800e+05 2.001996e+07 -3.763754e+08
#> [4,] 1.490400e+04 5.022000e+05 1.621004e+08 -9.465715e+09 -4.582619e+12
#> [5,] 1.506600e+06 7.963304e+08 -1.449162e+11 -6.064864e+13 -1.066586e+16
#> [6,] 2.388991e+09 -1.289960e+12 -3.833029e+14 -6.622754e+16 -6.183356e+19
#> [7,] -3.869879e+12 -1.343957e+15 -3.420400e+17 -6.456986e+20 -7.998594e+22
#> [8,] -4.031871e+15 -7.217225e+17 -5.620753e+21 2.223168e+23 2.541624e+27
#> [9,] -2.165167e+18 -3.280432e+22 1.351517e+25 2.919678e+28 0.000000e+00
#> [10,] -9.841296e+22 1.334467e+26 2.027200e+29 0.000000e+00 0.000000e+00
#> [11,] 4.003401e+26 9.556987e+29 0.000000e+00 0.000000e+00 0.000000e+00
#> [12,] 2.867096e+30 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
#> [,6] [,7] [,8] [,9] [,10]
#> [1,] 1.608390e+05 1.416951e+06 -3.889467e+08 2.551458e+10 -7.647989e+12
#> [2,] -4.184314e+07 -6.519780e+09 -4.851746e+11 -5.443070e+14 -8.643787e+16
#> [3,] -2.104693e+11 -4.176750e+13 -1.919977e+16 -2.149281e+18 1.537431e+20
#> [4,] -1.028311e+15 -3.496619e+17 -3.965155e+19 4.033242e+21 0.000000e+00
#> [5,] -4.849558e+18 -7.341200e+20 1.517919e+23 0.000000e+00 0.000000e+00
#> [6,] -9.637761e+21 5.055024e+24 0.000000e+00 0.000000e+00 0.000000e+00
#> [7,] 1.388833e+26 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
#> [8,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
#> [9,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
#> [10,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
#> [11,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
#> [12,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
#> [,11] [,12]
#> [1,] -1.013917e+15 -1.558129e+17
#> [2,] 4.570022e+17 0.000000e+00
#> [3,] 0.000000e+00 0.000000e+00
#> [4,] 0.000000e+00 0.000000e+00
#> [5,] 0.000000e+00 0.000000e+00
#> [6,] 0.000000e+00 0.000000e+00
#> [7,] 0.000000e+00 0.000000e+00
#> [8,] 0.000000e+00 0.000000e+00
#> [9,] 0.000000e+00 0.000000e+00
#> [10,] 0.000000e+00 0.000000e+00
#> [11,] 0.000000e+00 0.000000e+00
#> [12,] 0.000000e+00 0.000000e+00