BESSELA

Fractional order Bessel functions and accuracy estimate.

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

J = 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.

For some values of the arguments, this computation is

severely contaminated by roundoff error.  Consequently

[J,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 J 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