Off[General::spell]  ;      Off[
      General::spell1]

m = 9;

(*          eps1,    
          eps2,     eps3  und    
          eps4  sind  vorgegenene  Konstanten            *)

eps1 = 0.001;    eps2 = 0.005;   eps3  =  0.01;    eps4 = 
      0.05;

x0 = 1.3;
For [  i := 1, i <= m, i++,  x[i]  =  i x0 ]
Table[ PaddedForm[x[i], 4] , {i, 1, m}]

a[0] = 1;
Do[ 
      a[i] = 1; 
Do[ 
        a[i - j] = a[i - j - 1] - x[i]*a[i - j], {j, 1, i - 1}]; 
      a[0] = -x[i]*a[0], {i, 1, m}]
Table[AccountingForm[PaddedForm[a[i], {16, 7}]], {i, 0, m}]

P[xx_] := (∏_(i = 1)^m)(xx - x[i])
 P[xx]

(*    Grenzen    für  die  x - 
          Werte    und  die  y - 
          Werte  in  der  Graphik  setzen    *)

xmin = 0;   xmax = 
      16;     ymin = -60000;     ymax = 70000;
<< Graphics`Colors`                       (*  Package zur Farbdefinition in der Graphik  *) 
Kurv[1]=Plot[ P[xx], {xx, xmin, xmax}, 
          PlotRange -> {{xmin, xmax}, {ymin, 
                ymax}}, 
PlotPoints -> 40, 
          AxesLabel -> { "-> X", "  ^ Y"},  
          PlotStyle -> Green];

S[xx_] := (∑_(i = 0)^m) a[i] (xx^i)
S[xx]

Kurv[2]=Plot[S[xx], {xx, xmin, xmax}, 
          PlotRange -> {{xmin, xmax}, { ymin, ymax}}, PlotPoints -> 40, 
          AxesLabel -> { "-> X", "  ^ Y"}, PlotStyle -> Red];

Hsum[xx_] = a[m]; 
Do [
      Hsum[xx_] = Hsum[xx]*xx + a[m - i], {i, 1, 
        m}]
Hsum[xx]

Kurv[3]=Plot[ Hsum[xx], {xx, xmin, xmax}, 
        PlotRange -> {{xmin, xmax}, { ymin, ymax}}, 
        AxesLabel -> { "-> X", "  ^ Y"}, PlotStyle -> Blue]

Do[ b[i] = a[i], {i, 0, m}]
b[m - 2] = a[m - 2] +  eps1;
S1[xx_] := (∑_(i = 0)^m) SetPrecision[b[i], 7] (xx^i)
 S1[xx]

Kurv[4]=Plot[ S1[xx], {xx, xmin, xmax}, 
        PlotRange -> {{xmin, xmax}, { ymin, ymax}}, 
        AxesLabel -> { "-> X", "  ^ Y"}, PlotStyle -> Brown]

Do[ c[i] = a[i], {i, 0, m}]
c[m - 2] = a[m - 2] +  eps2;
S2[xx_] := (∑_(i = 0)^m) SetPrecision[c[i], 7] (xx^i)
S2[xx]

Kurv[5]=Plot[ S2[xx], {xx, xmin, xmax}, 
        PlotRange -> {{xmin, xmax}, { ymin, ymax}}, 
        AxesLabel -> { "-> X", "  ^ Y"}, PlotStyle -> Magenta]

Do[ d[i] = a[i], {i, 0, m}]
d[m - 2] = a[m - 2] +  eps3;
S3[xx_] := (∑_(i = 0)^m) d[i] (xx^i)
S3[xx]

Kurv[6]=Plot[ S3[xx], {xx, xmin, xmax}, 
        PlotRange -> {{xmin, xmax}, { ymin, ymax}}, 
        AxesLabel -> { "-> X", "  ^ Y"}, PlotStyle -> Apricot]

Do[ e[i] = a[i], {i, 0, m}]
e[m - 2] = a[m - 2] +  eps4;
S4[xx_] := (∑_(i = 0)^m) e[i] (xx^i)
  S4[xx]

Kurv[7]=Plot[ S4[xx], {xx, xmin, xmax}, 
        PlotRange -> {{xmin, xmax}, { ymin, ymax}}, 
        AxesLabel -> { "-> X", "  ^ Y"}, PlotStyle -> Brick]

DiSumPro[xx_] := S[xx] - P[xx]
 DiSumPro[xx]

dxmin = 0;   dxmax = 12;   dymin = -0.00003; 
      dymax = 0.00008;        neuer Maßstab !!! ;
Kurv[8]=Plot[ DiSumPro[xx], {xx, xmin, xmax}, 
        PlotRange -> {{xmin, xmax}, { dymin, dymax}}, 
        AxesLabel -> { "-> X", "  ^ Y"}, PlotPoints -> 40, 
        PlotStyle -> HotPink]

DiHomPro[xx_] := Hsum[xx] - P[xx]
DiHomPro[xx]

Kurv[9]=Plot[ DiHomPro[xx], {xx, xmin, xmax}, 
        PlotRange -> {{xmin, xmax}, { dymin, dymax}}, 
        AxesLabel -> { "-> X", "  ^ Y"}, PlotPoints -> 40, 
        PlotStyle -> Cobalt]

DiS1mPro[xx_] := S1[xx] - P[xx]
DiS1mPro[xx]

pdiffmin=0; pdiffmax = 50000;         
Kurv[10]=Plot[ DiS1mPro[xx], {xx, xmin, xmax}, 
        PlotRange -> {{xmin, xmax}, {pdiffmin, pdiffmax}}, 
        AxesLabel -> { "-> X", "  ^ Y"}, PlotStyle -> Orange]

DiS2mPro[xx_] := S2[xx] - P[xx]
DiS2mPro[
      xx]
Kurv[11]=Plot[ DiS2mPro[xx], {xx, xmin, xmax}, 
        PlotRange -> {{xmin, xmax}, { pdiffmin, pdiffmax}}, 
        AxesLabel -> { "-> X", "  ^ Y"}, 
        PlotStyle -> ForestGreen]

DiS3mPro[xx_] := S3[xx] - P[xx]
DiS3mPro[
      xx]
Kurv[12]=Plot[ DiS3mPro[xx], {xx, xmin, xmax}, 
        PlotRange -> {{xmin, xmax}, {pdiffmin, pdiffmax}}, 
        AxesLabel -> { "-> X", "  ^ Y"}, 
        PlotStyle -> IndianRed]

liste1 = {Green, Red, Blue, HotPink, Brown, Magenta, Brick, Apricot, 
          DarkGreen, Cobalt, Orange, IndianRed, ForestGreen};

DiS4mPro[xx_] := S4[xx] - P[xx]
DiS4mPro[
      xx]
Kurv[13]=Plot[ DiS4mPro[xx], {xx, xmin, xmax}, 
        PlotRange -> {{xmin, xmax}, { pdiffmin, pdiffmax}}, 
        AxesLabel -> { "-> X", "  ^ Y"}, 
        PlotStyle -> DarkGreen]

Show[ Kurv[1], Kurv[2], Kurv[3], Kurv[4], Kurv[5], Kurv[6], 
      Kurv[7]]

Show[Kurv[8], Kurv[9]]

Show[Kurv[10], Kurv[11], Kurv[12], Kurv[13]]

diffxmin = -0.010; diffxmax = 0.5; 
        diffymin = -0.000000002; diffymax = 0.000000003;           
Plot[ { DiSumPro[xx], DiHomPro[xx], DiS1mPro[xx], DiS2mPro[xx]}, {xx, 
        diffxmin, 
        diffxmax}, 
PlotRange -> {{diffxmin, 
            diffxmax}, { diffymin, diffymax}}, 
      AxesLabel -> { "-> X", "  ^ Y"}, PlotPoints -> 40,  
      PlotStyle -> { HotPink, Cobalt, Orange, ForestGreen }]

Plot[{ DiSumPro[xx], DiHomPro[xx], DiS1mPro[xx]}, {xx, 0, 12}, 
      PlotPoints -> 100, 
      PlotRange -> {{0, 2}, {-0.000000005, 0.000000005}}, 
      AxesLabel -> { "-> X", "  ^ Y"}, 
      PlotStyle -> {HotPink, Cobalt, Orange}]

xplmin = 11.6999999999;   xplmax = 11.7000000001;         
Kurv[14]=Plot[{P[xx], S[xx], Hsum[xx] }, {xx, xplmin - 0.0000049998, 
          xplmax + 0.0000011}, 
        PlotRange -> {{xplmin, xplmax}, {-0.000000006, 0.000000006}}, 
        AxesLabel -> { "-> X", "  ^ Y"}, 
        PlotStyle -> {Green, Red, Blue}]