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- (*start*)Clear[A, B, a, b, x];
- z = 4;
- x = (x1 - z);
- Expand[1 + 2 x + x^2/2 + x^3/2 + x^4/6]
- a1 = CoefficientList[%, x1]*Range[0, 4]!
- a = Flatten[{a1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0}];
- nn = Length[a];
- d = Max[Flatten[Position[Sign[Abs[a]], 1]]]
- A = Table[
- Table[If[n >= k, Binomial[n - 1, k - 1]*a[[n - k + 1]], 0], {k, 1,
- Length[a]}], {n, 1, Length[a]}];
- b = Inverse[A][[All, 1]];
- x = N[Table[(n - 1)*b[[n - 1]]/b[[n]], {n, nn - 8, nn - 1}], 30]
- Sum[a[[k + 1]]/k!*x^k, {k, 0, d}]
- -z + x
- Clear[x];
- Sum[a[[k + 1]]/k!*x^k, {k, 0, d}]
- NSolve[1 + 2 x + x^2/2 + x^3/2 + x^4/6, x]
- (*end*)
- This program gives the first root for z =
- 4 as - z + x by limiting ratios : -3.0842859641660889018019
- (*start*)Clear[A, B, a, b, x];
- z = 0;
- x = (x1 - z);
- Expand[1 + 2 x + x^2/2 + x^3/2 + x^4/6]
- a1 = CoefficientList[%, x1]*Range[0, 4]!
- a = Flatten[{a1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0}];
- nn = Length[a];
- d = Max[Flatten[Position[Sign[Abs[a]], 1]]]
- A = Table[
- Table[If[n >= k, Binomial[n - 1, k - 1]*a[[n - k + 1]], 0], {k, 1,
- Length[a]}], {n, 1, Length[a]}];
- b = Inverse[A][[All, 1]];
- x = N[Table[(n - 1)*b[[n - 1]]/b[[n]], {n, nn - 8, nn - 1}], 30]
- Sum[a[[k + 1]]/k!*x^k, {k, 0, d}]
- -z + x
- Clear[x];
- Sum[a[[k + 1]]/k!*x^k, {k, 0, d}]
- NSolve[1 + 2 x + x^2/2 + x^3/2 + x^4/6, x]
- (*end*)
- and the second root for z =
- 0 as - z +
- x also by limiting ratios : -0.5406916617670971775777849727
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