Growing the Digital Repository of Mathematical Formulae with Generic LaTex Sources
One initial goal for the DRMF is to seed our digital compendium with fundamental orthogonal polynomial formulae. We had used the data from the NIST Digital Library of Mathematical Functions (DLMF) as initial seed for our DRMF project. The DLMF input LaTeX source already contains some semantic information encoded using a highly customized set of semantic LaTeX macros. Those macros could be converted to content MathML using LaTeXML. During that conversion the semantics were translated to an implicit DLMF content dictionary. This year, we have developed a semantic enrichment process whose goal is to infer semantic information from generic LaTeX sources. The generated context-free semantic information is used to build DRMF formula home pages for each individual formula. We demonstrate this process using selected chapters from the book “Hypergeometric Orthogonal Polynomials and their q-Analogues” (2010) by Koekoek, Lesky and Swarttouw (KLS) as well as an actively maintained addendum to this book by Koornwinder (KLSadd). The generic input KLS and KLSadd LaTeX sources describe the printed representation of the formulae, but does not contain explicit semantic information. See http://drmf.wmflabs.org.
KeywordsOrthogonal Polynomial Semantic Information Hypergeometric Orthogonal Polynomial Seeding Project Substitution Formula
(The mention of specific products, trademarks, or brand names is for purposes of identification only. Such mention is not to be interpreted in any way as an endorsement or certification of such products or brands by the National Institute of Standards and Technology, nor does it imply that the products so identified are necessarily the best available for the purpose. All trademarks mentioned herein belong to their respective owners.) We are indebted to Wikimedia Labs, the XSEDE project, Springer-Verlag, the California Institute of Technology, and Wolfram Research Inc. for their contributions and continued support. We would also like to thank Roelof Koekoek, Tom Koornwinder, Roberto Costas-Santos, Eric Weisstein, Dan Lozier, Alan Sexton, Bruce Miller, Abdou Youssef, Charles Clark, Volker Markl, George Andrews, Mourad Ismail, and Dmitry Karp for their advice, invaluable assistance, and support.
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