Bug [1954846] bessel_i(1/2,0) -> divide by zero error



Thanks for working on the numerical evaluation of Bessel functions.

I see that you are returning "infinity" at singularities.  This is not
correct in Maxima, because (unfortunately) Maxima does not simplify
expressions involving infinity correctly.  For example,
infinity-infinity => 0 and infinity/infinity => 1.  Thus, to avoid
incorrect calculations, it is important to give an error rather than
returning a value in these cases.  This is what is done for, e.g.
tan(%pi/2). You might think that we could use IEEE infinities, but
there, too, there are problems, as the various Maxima/Lisp
combinations do not in general handle IEEE infinities correctly.

            -s