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# Untitled

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1. NN = 300; n = 30; M = 5;
2. k = a*(M + 1)^2/NN;
3. ei[l_] := 1 + 2*k*Cos[Pi*l/(M + 1)] - 2*k;
4. prod = 1;
5. For[l = 1, l <= M, l++,
6.   prod = prod*ei[l];
7.   ];
8. dA = Simplify[prod];
9. R = ConstantArray[0, {M, M}];
10. For[jj = 1, jj <= M, jj++,
11. For[l = 1, l <= M, l++,
12.     R[[jj, l]] = Sin[l*Pi*jj/(M + 1)];
13.     ];
14.   ];
15. Q = Simplify[Sqrt[2/(M + 1)]*R];
16. Dinvn = ConstantArray[0, {M, M}];
17. For[l = 1, l <= M, l++,
18.   Dinvn[[l, l]] = 1/ei[l]^n;
19.   ];
20. Ainvn = Q.Dinvn.Transpose[Q];
21. dAi = 1/dA^n;
22. f[x_] := PDF[
23.    ProductDistribution[NormalDistribution[0, 1],
24.    NormalDistribution[0, 1], NormalDistribution[0, 1],
25.    NormalDistribution[0, 1], NormalDistribution[0, 1]], x];
26. w = {x[1], x[2], v, x[4], x[5]};
27. integrand = f[Ainvn.w]*dAi;
28. NIntegrate[integrand /. v -> 1, {x[1], -[Infinity], [Infinity]},{x[2],-[Infinity],[Infinity]}, {x[4], -[Infinity], [Infinity]}, {x[5],-[Infinity], [Infinity]}, {a, 1, 2}]
29.
30. NIntegrate::izero: Integral and error estimates are 0 on all integration subregions. Try increasing the value of the MinRecursion option. If value of integral may be 0, specify a finite value for the AccuracyGoal option.
31.
32. 0.
33.
34. dAi /. a -> 1.4
35.
36. 2.06591*10^30
37.
38. Ainvn.w /. {x[1] -> 1, x[2] -> 1, x[4] -> 1, x[5] -> 1, a -> 1.5, v -> -0.5}
39.
40. {-6.71576*10^13, 1.1632*10^14, -1.34315*10^14, 1.1632*10^14, -6.71576*10^13}
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