학술논문
Computing the Hilbert transform of the generalized Laguerre and Hermite weight functions.
Document Type
Journal
Author
Gautschi, Walter (1-PURD-C) AMS Author Profile; Waldvogel, Jörg (CH-ETHZ-AM) AMS Author Profile
Source
Subject
65 Numerical analysis -- 65R Integral equations, integral transforms
65R10Integral transforms
65R10
Language
English
Abstract
Summary: ``Explicit formulae are given for the Hilbert transform $\intslash_{\Bbb R}w(t)dt/(t-x)$, where $w$ is either the generalized Laguerre weight function $w(t)=0$ if $t\leq 0$, $w(t)=t^\alpha e^{-t}$ if $0-1,\ x>0$, or the Hermite weight function $w(t)=e^{-t^2}$, $-\infty