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.
See also BESSEL1HHH2WN, BESSELJ , BESSELI .
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:
x 25 | 11.8 14.4
75 | 14.5 1.9