On the asymptotics and zeros of a class of Fourier integrals

Authors

  • Richard Bruce Paris University of Abertay Dundee Dundee DD1 1HG UK

Keywords:

Fourier integrals, asymptotic expansion, zeros, Wright function

Abstract

We obtain the asymptotic expansion of the Fourier integrals
\[\int_0^\infty t^{\nu-1}\, \raisebox{-.8ex}{\mbox{$\stackrel{\textstyle\cos}{\sin}$}}\,(xt) \,\exp\,(-t^n/n)\,dt\]
for large complex values of $x$ and integer $n>2$ by means of the asymptotic theory of the
Wright function. Asymptotic approximations for both the real and complex zeros of these integrals
are considered.
These results are extended to $p$-dimensional Fourier integrals of a similar structure.

Author Biography

  • Richard Bruce Paris, University of Abertay Dundee Dundee DD1 1HG UK
    Emeritus Reader in Mathematics

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Published

2012-07-31

Issue

Vol. 5 No. 3: (July 2012)

Section

Complex Analysis

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How to Cite

On the asymptotics and zeros of a class of Fourier integrals. (2012). European Journal of Pure and Applied Mathematics, 5(3), 260-281. https://www.ejpam.com/index.php/ejpam/article/view/1206