Über asymptotische Erzeugende rekursiv definierter Funktionen
type: Item
instance of: scholarly article
title: Über asymptotische Erzeugende rekursiv definierter Funktionen
zbMATH Open document ID: 0642.33025
DOI: 10.1007/BF01838154
author: Franz Pittnauer
author: Norbert Runge
published in: Aequationes Mathematicae
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137252
review text: To an arbitrary sequence of real functions a so-called asymptotic generating function is associated. This is a function possessing an asymptotic power series the coefficients of which are the given sequence of functions. Using a theorem of Ritt in the theory of asymptotic power series, it is shown that this always is possible. In the case where the sequence is recursively defined the asymptotic generating function turns out as a solution to a specific equation which may be a linear algebraic equation, ordinary difference equation of first order or partial differential equations of first or second order. A lot of special functions are covered by this method.
Mathematics Subject Classification ID: 33E99
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 41A60
zbMATH DE Number: 4046146
reviewed by: Heinrich Begehr
MaRDI profile type: Publication
cites work: Q5618583
cites work: Vorlesungen über asymptotische Reihen
cites work: A SOLUTION OF THE NAVIER–STOKES EQUATIONS ILLUSTRATING THE RESPONSE OF A LAMINAR BOUNDARY LAYER TO A GIVEN CHANGE IN THE EXTERNAL STREAM VELOCITY
cites work: Group-theoretic origin of certain generating functions
OpenAlex ID: W2067814601
description: scientific article; zbMATH DE number 4046146