To get back to the question of argument order, it seems strange to me
that
pari(2).besselk(3)
should meant K_2(3) rather than K_3(2).

sage: pari(2).besselk(3)
0.06151045847174203765682007145
sage: bessel_K(2,3)
0.0615104584717420

bessel_K(nu,x) is written K_nu(x) because the first argument nu is in
some sense a parameter - in many cases an integer - identifying
K_nu as the nu'th Bessel function of type K.  So I would naively
imagine that
pari(2).besselk(3)
would mean `take the 3rd bessel function and apply it to 2'.

Is there some general philosophy that dictates the opposite behavior?
Like, say, "f(x,y) always translates to x.f(y)"?

As a preview of an issue I'll raise in a separate post, note that Sage
is not giving us its best with bessel_K:

sage: bessel_K(2+I,3+I)
Traceback (most recent call last):
...
TypeError: Unable to convert x
(='0.043192827269587267-0.040059538066532876*I') to real number.

The answer here is correct, and the only problem is that Sage was
expecting the result to be a real number.

Cheers,

Peter
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