Remarks on Slater's asymptotic expansions of Kummer functions for large values of the a-parameter

2013/06/22 by Nico Μ. Τemme, Temme, Nico M
Computer Science · Engineering · Mathematics · #33B20 #33C15 #41A60 #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1306.5328

openalex publication_date 2013/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In Slater's 1960 standard work on confluent hypergeometric functions, also called Kummer functions, a number of asymptotic expansions of these functions can be found. We summarize expansions derived from a differential equation for large values of the a-parameter. We show how similar expansions can be derived by using integral representations, and we observe discrepancies with Slater's expansions.

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