m=1 (n=3): a=0.25 b=0.5  F=f(b)=0.374182345504  rho0=h(b)=1.125000000000 (1+(b-a)/2=1.125000000000)  c=-0.625000
    max m f h^(m-1) on [a,b] = 0.374182 <= bound 0.500000 < 1;  Sc on [a,b]: min 0, max 29.1192;  max|F1-F3| (interior) = 9.11e-09
    core Sc (r<a) = m(m-1) = 0;  end Sc (r>b) = 0;  grid points where phi' underflows to 0: 10;  grid checks: True
m=2 (n=4): a=0.125 b=0.25  F=f(b)=0.187088345621  rho0=h(b)=1.062500000000 (1+(b-a)/2=1.062500000000)  c=-0.812500
    max m f h^(m-1) on [a,b] = 0.397563 <= bound 0.531250 < 1;  Sc on [a,b]: min 0, max 117.966;  max|F1-F3| (interior) = 1.37e-07
    core Sc (r<a) = m(m-1) = 2;  end Sc (r>b) = 0;  grid points where phi' underflows to 0: 10;  grid checks: True
m=3 (n=5): a=0.0833333 b=0.166667  F=f(b)=0.124724924471  rho0=h(b)=1.041666666667 (1+(b-a)/2=1.041666666667)  c=-0.875000
    max m f h^(m-1) on [a,b] = 0.406006 <= bound 0.542535 < 1;  Sc on [a,b]: min 0, max 266.566;  max|F1-F3| (interior) = 6.87e-07
    core Sc (r<a) = m(m-1) = 6;  end Sc (r>b) = 0;  grid points where phi' underflows to 0: 10;  grid checks: True
m=4 (n=6): a=0.0625 b=0.125  F=f(b)=0.093543452033  rho0=h(b)=1.031250000000 (1+(b-a)/2=1.031250000000)  c=-0.906250
    max m f h^(m-1) on [a,b] = 0.410360 <= bound 0.548355 < 1;  Sc on [a,b]: min 0, max 474.916;  max|F1-F3| (interior) = 2.16e-06
    core Sc (r<a) = m(m-1) = 12;  end Sc (r>b) = 0;  grid points where phi' underflows to 0: 10;  grid checks: True
m=6 (n=8): a=0.0416667 b=0.0833333  F=f(b)=0.062362139759  rho0=h(b)=1.020833333333 (1+(b-a)/2=1.020833333333)  c=-0.937500
    max m f h^(m-1) on [a,b] = 0.414807 <= bound 0.554299 < 1;  Sc on [a,b]: min 0, max 1070.87;  max|F1-F3| (interior) = 1.09e-05
    core Sc (r<a) = m(m-1) = 30;  end Sc (r>b) = 0;  grid points where phi' underflows to 0: 10;  grid checks: True
m=10 (n=12): a=0.025 b=0.05  F=f(b)=0.037417205977  rho0=h(b)=1.012500000000 (1+(b-a)/2=1.012500000000)  c=-0.962500
    max m f h^(m-1) on [a,b] = 0.418434 <= bound 0.559146 < 1;  Sc on [a,b]: min 0, max 2979.8;  max|F1-F3| (interior) = 8.40e-05
    core Sc (r<a) = m(m-1) = 90;  end Sc (r>b) = 0;  grid points where phi' underflows to 0: 10;  grid checks: True
m=20 (n=22): a=0.0125 b=0.025  F=f(b)=0.018708573692  rho0=h(b)=1.006250000000 (1+(b-a)/2=1.006250000000)  c=-0.981250
    max m f h^(m-1) on [a,b] = 0.421194 <= bound 0.562836 < 1;  Sc on [a,b]: min 0, max 11934.7;  max|F1-F3| (interior) = 1.34e-03
    core Sc (r<a) = m(m-1) = 380;  end Sc (r>b) = 0;  grid points where phi' underflows to 0: 10;  grid checks: True
exact: (1/2)(1+1/(8m))^(m-1) < 1 for m=1..2000: True (all m: (1+1/(8m))^(m-1) < e^(1/8) < 2 because e < 2^8)
ALL NUMERIC CHECKS PASSED
