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- (*Program 2*)
- (*The limiting ratio of the form (n-1)*a (n-1)/a(n) applied to the \
- first column of the matrix inverse of the binomial matrix multiplied \
- elementwise with the coefficients in the Taylor polynomial of the \
- Riemann zeta function,expanded at an arbitrary point in the critical \
- strip (with imaginary part greater than 10),appended with trailing \
- zeros.The trailing zeros...0,0,0,0,0,0,0,... in the vector "a" give \
- better convergence to the Riemann zeta zeros*)
- (*start*)
- Clear[start, end, realPart, zz, d, digits, a, nn, A, n, k, b, z, list,
- x];
- start = 10;
- end = 60;
- realPart = 0;
- (*realPart=1/2;*)
- (*realPart=1;*)
- (*d must be much greater than zz*)
- Monitor[list = Table[zz = 20;
- d = 40;
- digits = 30;
- a = Flatten[{CoefficientList[
- Normal[Series[(1 - x - x^2), {x, 0, zz}]], x]*Range[0, 2]!,
- Range[d]*0}];
- nn = Length[a];
- A = Table[
- Table[If[n >= k, Binomial[n - 1, k - 1]*a[[n - k + 1]], 0], {k,
- 1, Length[a]}], {n, 1, Length[a]}];
- Quiet[b = Inverse[A][[All, 1]]];
- 0*z*I + N[(nn - 1)*b[[nn - 1]]/b[[nn]], digits], {z, start, end,
- 1/10}], z*10]
- "Plot of the real part:"
- ListLinePlot[Re[list], PlotRange -> {-1, 3}, DataRange -> {start, end}]
- "Plot of the imaginary part:"
- ListLinePlot[Im[list], DataRange -> {start, end}]
- (*end*)
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