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BibTeX entry
@Article{Pegoraro:2011:ECV,
author = "Vincent Pegoraro and Philipp Slusallek",
title = "On the Evaluation of the Complex-Valued Exponential
Integral",
journal = j-J-GRAPHICS-GPU-GAME-TOOLS,
volume = "15",
number = "3",
pages = "183--198",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1080/2151237X.2011.617177",
ISSN = "2151-2272 (print), 2151-237X (electronic)",
ISSN-L = "2151-2272",
bibdate = "Wed Dec 14 10:31:39 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/jgraphtools.bib",
abstract = "Although its applications span a broad scope of
scientific fields ranging from applied physics to
computer graphics, the exponential integral is a
nonelementary special function available in specialized
software packages but not in standard libraries,
consequently requiring custom implementations on most
platforms. In this paper, we provide a concise and
comprehensive description of how to evaluate the
complex-valued exponential integral. We first introduce
some theoretical background on the main characteristics
of the function, and outline available third-party
proprietary implementations. We then provide an
analysis of the various known representations of the
function and present an effective algorithm allowing
the computation of results within a desired accuracy,
together with the corresponding pseudocode in order to
facilitate portability onto various systems. An
application to the calculation of the closed-form
solution to single light scattering in homogeneous
participating media illustrates the practical benefits
of the provided implementation with the hope that, in
the long term, the latter will contribute to
standardizing the availability of the complex-valued
exponential integral on graphics platforms.",
acknowledgement = ack-nhfb,
journal-URL = "http://www.tandfonline.com/loi/ujgt20",
onlinedate = "21 Oct 2011",
}
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