Gauss-Legendre Quadrature of order 10

Code:
// Local function to integrate

MYFX(x)

BEGIN

  RETURN 1/x;

END;

  

EXPORT GaussQuad10(a,b,h)

BEGIN

  // Gauss-Legendre 10th Order Quadrature

  // HP Prime Calculator Program

  

  LOCAL  I, S, C, D;

  LOCAL Xn, W, T, b1, Stot;

  

  IF h <= 0 OR h > (b - a) THEN

    h = b - a;

  END;

  

  // Initialize arrays for 10 points

  Xn := MAKELIST(0, I, 1, 10);

  W := MAKELIST(0, I, 1, 10);

  T := MAKELIST(0, I, 1, 10);

  

 

  // Standard Gauss-Legendre nodes on [-1,1]

  T(1) := -0.9739065285171717;

  T(2) := -0.8650633666889845;

  T(3) := -0.6794095682990244;

  T(4) := -0.4333953941292472;

  T(5) := -0.1488743389816312;

  T(6) := 0.1488743389816312;

  T(7) := 0.4333953941292472;

  T(8) := 0.6794095682990244;

  T(9) := 0.8650633666889845;

  T(10) := 0.9739065285171717;

  

  // Gauss-Legendre weights

  W(1) := 0.0666713443086881;

  W(2) := 0.1494513491505806;

  W(3) := 0.2190863625159820;

  W(4) := 0.2692667193099963;

  W(5) := 0.2955242247147529;

  W(6) := 0.2955242247147529;

  W(7) := 0.2692667193099963;

  W(8) := 0.2190863625159820;

  W(9) := 0.1494513491505806;

  W(10) := 0.0666713443086881;

  Stot := 0;

  

  WHILE a < b DO

    b1 := a + h;

    // Transform nodes from [-1,1] to [a,b1]

    C := (b1 - a) / 2;

    D := (a + b1) / 2;

  

    FOR I FROM 1 TO 10 DO

      Xn(I) := C * T(I) + D;

    END;

  

    // Compute integral using Gauss-Legendre quadrature

    S := 0;

    FOR I FROM 1 TO 10 DO

      S := S + W(I) * MYFX(Xn(I));

    END;

    Stot := Stot +  C * S;

    a := a + h

  END;

  

  RETURN Stot;

END;