
 ╔══════════════════════════════════════╗   (C) Copyright 1986-1990
 ║  INTG.EXE - The Integration machine  ║         Zvi Shippony
 ╚══════════════════════════════════════╝        (818) 990-0134

 Option 1
 ---------
    Either Romberg's or Adaptive Gauss-Legendre method.

  Sub option: R
  -------------

    Romberg's method is used. If the interval in infinite, a change of
 variable is done: z = Arctan(x), thus F(x)dx  -->  F(tan(z))dz/cos²(z)
 and the limits of integration are changed appropriately.

    If there is no singularity at any of the limits, the routine uses
 up to 2^14 = 16384 sub-divisions, otherwise, the routine switches to
 Mid-Point Method with up to 3^9 = 19683  sub-divisions.

$$

  Sub option: A
  -------------

    Adaptive Gauss-Legendre method. The interval is handled piece by
 piece, and the Gauss-Legendre method (16 points) is used on each
 sub-interval. The interval is cut in half in case of non-convergance.

    This process is continued until the entire interval is handled.

$$

 Option 2
 ---------
  For Gauss's type procedure over a FINITE interval, two options exists:

    Sub option G: Gauss-Legendre , weight function W(x) ≡ 1.0

    Sub option C: Gauss-Chebyshev, weight function W(x) ≡ Sqrt((x-a)*(b-x))
                  (W(x) ≡ 1.0/Sqrt((x-a)*(b-x)) also works ..)
                  ( Here [a,b] is the integration interval )

  For Gauss's type procedure over a INFINITE interval, two options exists:

    Sub option L: Gauss-Laguerre , weight function W(x) ≡ Exp(-x)

    Sub option H: Gauss-Hermite  , weight function W(x) ≡ Exp(-x²)

 ** Note:

  Legendre,Chebyshev and Hermite Quadratures uses 16 points formula .
  Laguerre Quadrature uses 25 points formula .

$$
  For options 1 & 2 - F(x) is any expression in the variable: X

     Expression is any legal combination of: +, -, *, /, **, !, (, )
     and any of the following functions:

   ABS, INT, EXP, SIN, COS, TAN, COT, LOG, LN, FACT or ! (Factorial), SIGN,
   SQRT, SINH, COSH, TANH, ARCSIN, ARCCOS, ARCTAN, ARCSINH, ARCCOSH, ARCTANH

   And the "Special Functions" :

     Z(x)     { Riemann's Zeta function }
     G(x)     { Gamma function, (IF x is an integer then x! = G(x+1)) }
     BJ(n,x)  { Bessel Function of the  first kind, J(n,x) }
     BY(n,x)  { Bessel Function of the second kind, Y(n,x) }
     BI(n,x)  { Modified Bessel Function of the  first kind, I(n,x) }
     BK(n,x)  { Modified Bessel Function of the second kind, K(n,x) }
     SBJ(n,x) { Spherical Bessel Function of the  first kind, j(n,x) }
     SBY(n,x) { Spherical Bessel Function of the second kind, y(n,x) }

 ** Note:
      PI is a reserved name and will be interpeted as Pi = 3.14159265358...
$$

 Option 3
 ---------
    Program RINTG.EXE is called to perform the integration. It has its own
 help option, so activate option 3 and then ask for help.

 Option 4
 ---------
    Program WINTG.EXE is called to perform the actions. It has its own help
 option, so activate option 4 and then ask for help.


                            That's all folks ...

