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May 21st, 2025
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  1. clear, clc, close all;
  2. syms x
  3. n=11;
  4. f(x)=cos(pi*x/2);
  5. [v]=VECTORFV(n,f);
  6. p=1;
  7. for j=1:3:n
  8. p=p*v(j);
  9. end
  10. s1=0;
  11. for k=2:3:n
  12. s1=s1+(v(k));
  13. end
  14. s2=0;
  15. for k=3:3:n
  16. s2=s2+(v(k));
  17. end
  18. s=s1-s2;
  19.  
  20. z=p-s;
  21. disp(z)
  22. b=0;
  23. for k=3:3:n
  24. b=b+((((k-n/2)^(k/3))/(factorial(k/3))*v(k)));
  25. end
  26. g(x)=eval(f(n/2))+b;
  27.  
  28. fplot(f,[(n/2)-1,(n/2)+1], Color= 'r')
  29. hold on
  30. fplot(g,[(n/2)-1,(n/2)+1], Color= 'b')
  31.  
  32.  
  33.  
  34.  
  35.  
  36.  
  37.  
  38. function[v]= VECTORFV(n,f)
  39. syms x
  40. v=zeros(n,1);
  41. for k=1:3:n
  42. a=((-1)^k)/(k*(k+1)*(k+2));
  43. b=eval(int(f^k,x,0,n));
  44. v(k)=a*b;
  45. end
  46. for k=2:3:n
  47. a=((-1)^(k+1))/(k^3-k);
  48. b=eval(int(f,x,0,k));
  49. v(k)=a*b^n;
  50. end
  51. faux(x)=f(x);
  52. for k=3:3:n
  53. fa=diff(faux,x,k/3);
  54. v(k)=eval(fa(n/2));
  55. faux(x)=f(x);
  56. end
  57. end
  58.  
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