A fast algorithm for evaluation of normalized Hermite functions
An algorithm for computing the normalized Hermite Functions, h(n)(x) in floating point arithmetic is presented. The algorithm is based on an efficient numerical evaluation of certain closed contour integrals in the complex plane. For large degree n, the algorithm is significantly faster than the O(n) complexity of the well known three term recurrence relation. Comparable accuracy is achieved in no more than O(v n) operations, and for arguments bounded away from +/-root 2n, only O(root ln n) operations.
fast algorithm hermite functions recursion numerical integration