[Octave-bug-tracker] [bug #48307] sinc loses precision for large arguments

[Colin Macdonald]

Follow-up Comment #28, bug #48307 (project octave):

I looked more carefully at bessel functions: my example in #48316 is a bit
flawed: it only uses integer inputs.  The relative error is much larger for
nearby non-integer inputs.  Maybe my expectations really are out-of-line with
common practice here!  I apologize for the tone of my debate.

My reading about other tools:

[Zhang and Jin 1996] (Standard special function reference).  For jn(x), they
simply compute sin(x)/x in double precision for j0(x).  SciPy then uses this
algorithm via the fortran code "specfun".  For this reason, scipy's j0(pi*x)
agrees with Octave's sinc(z).

NR: for jn(x), they call their regular besselj function and scale with
sqrt(1/x)---the formula I mentioned below.

Matlab: seems to use sin(x)/x (b/c results match Octave's)

Boost: uses sin(x)/x for j0 and otherwise uses besselj.




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