
 ╔══════════════════════════════════════╗           (C) Copyright 1986-1990
 ║ MATHUTL.EXE - Math Utilities program ║                 Zvi Shippony
 ╚══════════════════════════════════════╝                (818) 990-0134

  For options 1,2,3 - enter 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)
   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...

  Example (options 1 - 3): Sqrt(3.0**X+12.25)-Exp(-Sin(X+1.0))

  Example (options 1 - 3): X - Int(Tan(X)+4.123)!

$$$
  Option 4:

  To compute a finite or infinite sum you need to use the SUM() function.
  The argument of the SUM function is any legal expression containing a
  running index letter (I,J,K,L,M  or: N). (Default index is: J) .

  You have the option to let the index run to 'Infinity' by specifying: 'Inf'
  or: 'Infinity'  for the index's limit. The actual limit will be:  32767  .

  Example: SUM(1.0/n^2) (for n = 1 to Infinity) will produce a result
           which is an approximation to Pi*Pi/6.0  ( 1.64493406684823.. )

  Example: SUM(X^k/k!)    (for k=0 to Inf) computes Exp(X) for a given X.

  Example: LN(SUM(1/k!))  (for k=0 to Inf) should give you 1.0

  Example: BJ(0,X)^2+2*SUM(BJ(k,X)^2) (k=1 to Inf) should give you: 1.0  for
           any X . This is a known identity involving J(n,x) (Bessel).

 ** NOTE: You can use more then one SUM() expression. For example:

               SUM(1/n^3) / (Sqrt(SUM(X/k!)))

$$$
  Option 5:

  Evaluate any leagal expression, given its argument(s). Note that there
  is no X or Y or any variable name here, all arguments are explicit.

  Example: Sqrt(3.0**6.2+12.25*BJ(2,4.5))-Exp(-Sin(SBY(3,2)*BK(1,6.2))



                            That's all folks ...
