An integral representation for the product of Airy functions
type: Item
instance of: scholarly article
title: An integral representation for the product of Airy functions
zbMATH Open document ID: 0879.33002
DOI: 10.1007/PL00001464
author: Olivier Vallée
author: Manuel Soares
author: Charles de Izarra
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1998-01-25T00:00:00Z
review text: Here the authors obtain the following integral representation for the product of two Airy functions \[ \text{Ai}(u) \text{Ai}(v)= \frac{1}{2\pi^{3/2}} \int_0^\infty \cos\Biggl(\frac{t^3}{12}+ \frac{u+v}{2}t- \frac{(u-v)^2}{4t}+ \frac{\pi}{4}\Biggr) \frac{dt}{t} \] which generalizes some results due to \textit{W. H. Reid} [ibid. 46, 159-170 (1995; Zbl 0824.33002)]. They also mention some particular cases and applications of this result.
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 1059770
zbMATH Keywords: Airy functions
reviewed by: Som Prakash Goyal
MaRDI profile type: Publication
full work available at URL: pl00001464
OpenAlex ID: W1988712833
description: scientific article; zbMATH DE number 1059770