Table B.1: Values of A (4th column) computed within the computer precision (double precision; about 16-digit) for different power law exponents s or s' (Cols 1 to 3) including those relevant for astrophysical applications (see also Fig. 5). Also given are the relative error on the coefficient (5th column) and the number of iterations (6th column) required.
s -3-s s' Coefficient A Relative error Iterations Comment

-4.00 +1.00 -2.50 -9.65735902799760E-02 +3.1E-15 6200 values of $A_\Delta$ and A₁

-3.95 +0.95 -2.45 -5.08795971306598E+00 +1.6E-16 4763

-3.90 +0.90 -2.40 -2.57897148688964E+00 +9.9E-17 6289

-3.85 +0.85 -2.35 -1.73622548292480E+00 +3.9E-17 8653

-3.80 +0.80 -2.30 -1.30966680644896E+00 +2.1E-17 10760

-3.75 +0.75 -2.25 -1.04923490407066E+00 +8.1E-17 7977

-3.70 +0.70 -2.20 -8.71529232712215E-01 +1.4E-16 7154

-3.65 +0.65 -2.15 -7.40760471984439E-01 +2.1E-16 6696

-3.60 +0.60 -2.10 -6.38987239513759E-01 +2.8E-16 6379

-3.55 +0.55 -2.05 -5.56193814181879E-01 +3.5E-16 6133

-3.50 +0.50 -2.00 -4.86319914494768E-01 +4.3E-16 5926

-3.45 +0.45 -1.95 -4.25454571886386E-01 +5.2E-16 5743

-3.40 +0.40 -1.90 -3.70931368062394E-01 +6.3E-16 5576

-3.35 +0.35 -1.85 -3.20839275213352E-01 +7.7E-16 5420

-3.30 +0.30 -1.80 -2.73740796314985E-01 +9.4E-16 5270

-3.25 +0.25 -1.75 -2.28500045775376E-01 +1.2E-15 5124

-3.20 +0.20 -1.70 -1.84171894656878E-01 +1.5E-15 4980

-3.15 +0.15 -1.65 -1.39926048201652E-01 +2.0E-15 4837

-3.10 +0.10 -1.60 -9.49911954664950E-02 +3.1E-15 4694

-3.05 +0.05 -1.55 -4.86101640289562E-02 +6.3E-15 4550

-3.00 +0.00 -1.50 -8.70956628336228E-15 +3.6E-02 4403 strictly 0 (see Appendix A)

-2.95 -0.05 -1.45 +5.16876888183838E-02 +6.4E-15 4252

-2.90 -0.10 -1.40 +1.07410381098617E-01 +3.2E-15 4098

-2.85 -0.15 -1.35 +1.68286941322651E-01 +2.1E-15 3937

-2.80 -0.20 -1.30 +2.35664501680007E-01 +1.6E-15 3771

-2.75 -0.25 -1.25 +3.11208301380443E-01 +1.2E-15 3596

-2.70 -0.30 -1.20 +3.97027142932255E-01 +1.0E-15 3410

-2.65 -0.35 -1.15 +4.95854560428368E-01 +8.6E-16 3212

-2.60 -0.40 -1.10 +6.11318936974807E-01 +7.4E-16 2997

-2.55 -0.45 -1.05 +7.48359798181055E-01 +6.5E-16 2759

-2.50 -0.50 -1.00 +9.13893162088934E-01 +5.7E-16 2486

-2.45 -0.55 -0.95 +1.11792019234452E+00 +5.1E-16 2151

-2.40 -0.60 -0.90 +1.37546760819327E+00 +4.5E-16 1662

-2.35 -0.65 -0.85 +1.71019225943660E+00 +4.1E-16 1335

-2.30 -0.70 -0.80 +2.16159222263118E+00 +3.7E-16 1821

-2.25 -0.75 -0.75 +2.80087471242395E+00 +3.4E-16 1997

-2.20 -0.80 -0.70 +3.77063202688011E+00 +3.1E-16 2058

-2.15 -0.85 -0.65 +5.40388067136072E+00 +2.8E-16 2036

-2.10 -0.90 -0.60 +8.70024086898869E+00 +2.6E-16 1928

-2.05 -0.95 -0.55 +1.86592556634413E+01 +2.4E-16 1681

-2.00 -1.00 -0.50 -1.38629436111989E+00 +7.2E-18 7955 values of $A_\Delta$ and A₁

-1.95 -1.05 -0.45 -2.14370823367682E+01 +2.1E-16 1770

-1.90 -1.10 -0.40 -1.14939346514465E+01 +1.9E-16 2141

-1.85 -1.15 -0.35 -8.22454216651923E+00 +1.8E-16 2399

-1.80 -1.20 -0.30 -6.63018820764787E+00 +1.7E-16 2598

-1.75 -1.25 -0.25 -5.71250114438470E+00 +1.7E-16 2755

-1.70 -1.30 -0.20 -5.14024384191494E+00 +1.6E-16 2878

-1.65 -1.35 -0.15 -4.77330268633758E+00 +1.6E-16 2972

-1.60 -1.40 -0.10 -4.54390925876444E+00 +1.5E-16 3039

-1.55 -1.45 -0.05 -4.41737401180816E+00 +1.5E-16 3078

-1.50 -1.50 +0.00 -4.37687923045294E+00 +1.5E-16 3091

-1.45 -1.55 +0.05 -4.41737401180816E+00 +1.5E-16 3078

**Table B.1:** Values of A (4th column) computed within the computer precision (double precision; about 16-digit) for different power law exponents s or s' (Cols 1 to 3) including those relevant for astrophysical applications (see also Fig. 5). Also given are the relative error on the coefficient (5th column) and the number of iterations (6th column) required.
s	-3-s	s'	Coefficient A	Relative error	Iterations	Comment
`-4.00`	`+1.00`	`-2.50`	`-9.65735902799760E-02`	`+3.1E-15`	`6200`	values of $A_\Delta$ and A₁
`-3.95`	`+0.95`	`-2.45`	`-5.08795971306598E+00`	`+1.6E-16`	`4763`
`-3.90`	`+0.90`	`-2.40`	`-2.57897148688964E+00`	`+9.9E-17`	`6289`
`-3.85`	`+0.85`	`-2.35`	`-1.73622548292480E+00`	`+3.9E-17`	`8653`
`-3.80`	`+0.80`	`-2.30`	`-1.30966680644896E+00`	`+2.1E-17`	`10760`
`-3.75`	`+0.75`	`-2.25`	`-1.04923490407066E+00`	`+8.1E-17`	`7977`
`-3.70`	`+0.70`	`-2.20`	`-8.71529232712215E-01`	`+1.4E-16`	`7154`
`-3.65`	`+0.65`	`-2.15`	`-7.40760471984439E-01`	`+2.1E-16`	`6696`
`-3.60`	`+0.60`	`-2.10`	`-6.38987239513759E-01`	`+2.8E-16`	`6379`
`-3.55`	`+0.55`	`-2.05`	`-5.56193814181879E-01`	`+3.5E-16`	`6133`
`-3.50`	`+0.50`	`-2.00`	`-4.86319914494768E-01`	`+4.3E-16`	`5926`
`-3.45`	`+0.45`	`-1.95`	`-4.25454571886386E-01`	`+5.2E-16`	`5743`
`-3.40`	`+0.40`	`-1.90`	`-3.70931368062394E-01`	`+6.3E-16`	`5576`
`-3.35`	`+0.35`	`-1.85`	`-3.20839275213352E-01`	`+7.7E-16`	`5420`
`-3.30`	`+0.30`	`-1.80`	`-2.73740796314985E-01`	`+9.4E-16`	`5270`
`-3.25`	`+0.25`	`-1.75`	`-2.28500045775376E-01`	`+1.2E-15`	`5124`
`-3.20`	`+0.20`	`-1.70`	`-1.84171894656878E-01`	`+1.5E-15`	`4980`
`-3.15`	`+0.15`	`-1.65`	`-1.39926048201652E-01`	`+2.0E-15`	`4837`
`-3.10`	`+0.10`	`-1.60`	`-9.49911954664950E-02`	`+3.1E-15`	`4694`
`-3.05`	`+0.05`	`-1.55`	`-4.86101640289562E-02`	`+6.3E-15`	`4550`
`-3.00`	`+0.00`	`-1.50`	`-8.70956628336228E-15`	`+3.6E-02`	`4403`	strictly 0 (see Appendix A)
`-2.95`	`-0.05`	`-1.45`	`+5.16876888183838E-02`	`+6.4E-15`	`4252`
`-2.90`	`-0.10`	`-1.40`	`+1.07410381098617E-01`	`+3.2E-15`	`4098`
`-2.85`	`-0.15`	`-1.35`	`+1.68286941322651E-01`	`+2.1E-15`	`3937`
`-2.80`	`-0.20`	`-1.30`	`+2.35664501680007E-01`	`+1.6E-15`	`3771`
`-2.75`	`-0.25`	`-1.25`	`+3.11208301380443E-01`	`+1.2E-15`	`3596`
`-2.70`	`-0.30`	`-1.20`	`+3.97027142932255E-01`	`+1.0E-15`	`3410`
`-2.65`	`-0.35`	`-1.15`	`+4.95854560428368E-01`	`+8.6E-16`	`3212`
`-2.60`	`-0.40`	`-1.10`	`+6.11318936974807E-01`	`+7.4E-16`	`2997`
`-2.55`	`-0.45`	`-1.05`	`+7.48359798181055E-01`	`+6.5E-16`	`2759`
`-2.50`	`-0.50`	`-1.00`	`+9.13893162088934E-01`	`+5.7E-16`	`2486`
`-2.45`	`-0.55`	`-0.95`	`+1.11792019234452E+00`	`+5.1E-16`	`2151`
`-2.40`	`-0.60`	`-0.90`	`+1.37546760819327E+00`	`+4.5E-16`	`1662`
`-2.35`	`-0.65`	`-0.85`	`+1.71019225943660E+00`	`+4.1E-16`	`1335`
`-2.30`	`-0.70`	`-0.80`	`+2.16159222263118E+00`	`+3.7E-16`	`1821`
`-2.25`	`-0.75`	`-0.75`	`+2.80087471242395E+00`	`+3.4E-16`	`1997`
`-2.20`	`-0.80`	`-0.70`	`+3.77063202688011E+00`	`+3.1E-16`	`2058`
`-2.15`	`-0.85`	`-0.65`	`+5.40388067136072E+00`	`+2.8E-16`	`2036`
`-2.10`	`-0.90`	`-0.60`	`+8.70024086898869E+00`	`+2.6E-16`	`1928`
`-2.05`	`-0.95`	`-0.55`	`+1.86592556634413E+01`	`+2.4E-16`	`1681`
`-2.00`	`-1.00`	`-0.50`	`-1.38629436111989E+00`	`+7.2E-18`	`7955`	values of $A_\Delta$ and A₁
`-1.95`	`-1.05`	`-0.45`	`-2.14370823367682E+01`	`+2.1E-16`	`1770`
`-1.90`	`-1.10`	`-0.40`	`-1.14939346514465E+01`	`+1.9E-16`	`2141`
`-1.85`	`-1.15`	`-0.35`	`-8.22454216651923E+00`	`+1.8E-16`	`2399`
`-1.80`	`-1.20`	`-0.30`	`-6.63018820764787E+00`	`+1.7E-16`	`2598`
`-1.75`	`-1.25`	`-0.25`	`-5.71250114438470E+00`	`+1.7E-16`	`2755`
`-1.70`	`-1.30`	`-0.20`	`-5.14024384191494E+00`	`+1.6E-16`	`2878`
`-1.65`	`-1.35`	`-0.15`	`-4.77330268633758E+00`	`+1.6E-16`	`2972`
`-1.60`	`-1.40`	`-0.10`	`-4.54390925876444E+00`	`+1.5E-16`	`3039`
`-1.55`	`-1.45`	`-0.05`	`-4.41737401180816E+00`	`+1.5E-16`	`3078`
`-1.50`	`-1.50`	`+0.00`	`-4.37687923045294E+00`	`+1.5E-16`	`3091`
`-1.45`	`-1.55`	`+0.05`	`-4.41737401180816E+00`	`+1.5E-16`	`3078`

Source LaTeX | All tables | In the text