2003/06/11 by Richard J. Mathar, Mathar, Richard J.
Mathematics · #33C15 #33E50 #33F05 #FOS: Mathematics #Mathematical and Theoretical Analysis #Numerical Analysis (math.NA) #advanced mathematical theories
paper · doi:10.48550/arxiv.math/0306184
openalex publication_date 2003/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Various approaches to the numerical representation of the Incomplete Gamma Function Fm(z) for complex arguments z and small integer indexes m are compared with respect to numerical fitness (accuracy and speed). We consider power series, Laurent series, Gautschi's approximation to the Faddeeva function, classical numerical methods of treating the standard integral representation, and others not yet covered by the literature. The most suitable scheme is the construction of Taylor expansions around nodes of a regular, fixed grid in the z-plane, which stores a static matrix of higher derivatives. This is the obvious extension to a procedure often in use for real-valued z.