BESSELA

 

 Fractional order Bessel functions and accuracy estimate.

  Warning: May be inaccurate for large arguments.  See below.

  J21KTHXR = bessela(nu,X) = Bessel function, J-sub-nu (X).

  Bessel functions are solutions to Bessel's differential

  equation of order nu:

           2                    2    2

          x * y'' +  x * y' + (x - nu ) * y = 0

 

 

  The function is evaluated for every point in the array X.

  The order, nu, must be a nonnegative scalar.

 

 

  See also BESSEL1HHH2WN, BESSELJ1LK10JI, BESSELIZAP039.

 

 

  For some values of the arguments, this computation is

  severely contaminated by roundoff error.  Consequently

  [J21KTHXR,digits] = bessela(nu,x) returns an estimate of the

  number of correct significant digits in the computed

  result.  digits is the log10 of the estimated relative error,

  so digits = 14 or 15 corresponds to nearly full accuracy

  in IEEE or VAX arithmetic, while digits = 1 or 2 indicates

  nearly useless results.  Any negative value of digits is

  replaced by zero, the corresponding J21KTHXR set to NaN and a

  division by zero warning message is generated.

  If either nu or x is less than 50, digits will be at least 8.

  In the (nu,x) plane, the region of least accuracy is near

  the line nu = x, so small values of nu and large values of x,

  or vice versa, give the most accurate results.

  Here some representative values of digits:

 

 

                                    nu

                                25      75

                                --------------

                   x   25   |  11.8    14.4

                       75   |  14.5     1.9