Q755951
type: Item
instance of: scholarly article
title: Asymptotische Entwicklungen der konfluenten hypergeometrischen Funktionen U(a,b,z) und M(a,b,z) für große Werte von b und z. (Asymptotic expansions of confluent hypergeometric functions U(a,b,z) and M(a,b,z) for large values of b and z)
zbMATH Open document ID: 0722.33002
DOI: 10.4171/ZAA/408
author: H.-J. Schell
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1990-01-01T00:00:00Z
review text: Asymptotic expansions are derived for the confluent hypergeometric functions U(a,b,z) and M(a,b,z). The parameter b and z are real and large. As is known, a transition point shows up when \(z\sim b\). Several publications are available for this asymptotic problem, in which parabolic cylinder functions are used to describe the phenomena. The present paper gives complete new expansions in terms of elementary functions for the case that \(y=z/b\) is fixed; \(y<1\) and \(y>1\) are treated separately. Later it is verified that the results include the cases \(b\to \infty\), z fixed and \(z\to \infty\), b fixed. Starting points for the investigations are the familiar integral representations of the Kummer functions.
Mathematics Subject Classification ID: 33C15
Mathematics Subject Classification ID: 41A60
zbMATH DE Number: 4190146
zbMATH Keywords: Whittaker function
zbMATH Keywords: confluent hypergeometric functions
reviewed by: Nico M. Temme
MaRDI profile type: Publication
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label: Asymptotische Entwicklungen der konfluenten hypergeometrischen Funktionen U(a,b,z) und M(a,b,z) für große Werte von b und z. (Asymptotic expansions of confluent hypergeometric functions U(a,b,z) and M(a,b,z) for large values of b and z)
description: scientific article; zbMATH DE number 4190146