The general approach for such problems to treat the Coulomb interaction separately from the short-ranged interaction, as the Coulomb problem can be solved exactly in terms of Coulomb functions, which take on the role of the Hankel functions in this problem.
12.
Clause 19 defines numerous special functions, including the gamma function, Riemann zeta function, beta function, exponential integral, logarithmic integral, sine integral, Fresnel integrals, error function, incomplete elliptic integrals, hypergeometric functions, Legendre polynomials, spherical harmonics, Hermite polynomials, Laguerre polynomials, Chebyshev polynomials, Bessel functions, Neumann functions, Hankel functions and Airy functions.
