Because the coefficients in (18.34.4) are not all positive, the polynomials cannot be orthogonal on the line with respect to a positive weight function. There is orthogonality on the unit circle, however:
the integration path being taken in the positive rotational sense.
where primes denote derivatives with respect to .
For uniform asymptotic expansions of as in terms of Airy functions (§9.2) see Wong and Zhang (1997) and Dunster (2001c). For uniform asymptotic expansions in terms of Hermite polynomials see López and Temme (1999b).
For further information on Bessel polynomials see §10.49(ii).