Natural Logarithm of Bessel Function, Overflow

Question

I am trying to calculate the logarithm of a modified Bessel function of second type in MATLAB, i.e. something like that:

log(besselk(nu, Z)) 

where e.g.

nu = 750;
Z = 1;

I have a problem because the value of log(besselk(nu, Z)) goes to infinity, because besselk(nu, Z) is infinity. However, log(besselk(nu, Z)) should be small indeed.

I am trying to write something like

f = double(sym('ln(besselk(double(nu), double(Z)))'));

However, I get the following error:

Error using mupadmex Error in MuPAD command: DOUBLE cannot convert the input expression into a double array. If the input expression contains a symbolic variable, use the VPA function instead.

Error in sym/double (line 514) Xstr = mupadmex('symobj::double', S.s, 0)`;

How can I avoid this error?

Answer 1

You're doing a few things incorrectly. It makes no sense to use double for your two arguments to to besselk and the convert the output to symbolic. You should also avoid the old string based input to sym. Instead, you want to evaluate besselk symbolically (which will return about 1.02×10²⁰⁵⁵, much greater than realmax), take the log of the result symbolically, and then convert back to double precision.

The following is sufficient – when one or more of the input arguments is symbolic, the symbolic version of besselk will be used:

f = double(log(besselk(sym(750), sym(1))))

or in the old string form:

f = double(sym('log(besselk(750, 1))'))

If you want to keep your parameters symbolic and evaluate at a later time:

syms nu Z;
f = log(besselk(nu, Z))
double(subs(f, {nu, Z}, {750, 1}))

Make sure that you haven't flipped the nu and Z values in your math as large orders (nu) aren't very common.