Methods for incomplete Bessel function evaluation

Abstract

AbstractPresented here are detailed methods for evaluating the incomplete Bessel functions arising when Gaussian‐type orbitals are used for systems periodic in one spatial dimension. The scheme is designed to yield these incomplete Bessel functions with an absolute accuracy of ±1 × 10−10, for the range of integer orders 0 ≤ n ≤ 12 [a range sufficient for a basis whose members have angular momenta of up to three units (s, p, d, or f atomic functions)]. To reach this accuracy level within acceptable computation times, new rational approximations were developed to compute the special functions involved, namely, the exponential integral E1(x) and the modified Bessel functions K0(x) and K1(x), to absolute accuracy ±1 × 10−15. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009