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1: Marjorie A. McClain
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► 1956 in Ithaca, New York) is a mathematician in the Applied and Computational Mathematics Division of NIST where she has provided support for mathematical software libraries and assisted with numerical computing projects since 1979.
More recently she has become an expert in the use of LaTeX and BibTex, and she has applied those skills in the preparation of the Latex documents for the DLMF chapters and in the development of the DLMF bibliography.
She is the Associate Technical Editor for the DLMF project when she retired in September, 2021.
►McClain received a degree in mathematics from Bucknell University in 1978 and an M.
…in mathematics from the University of Maryland, College Park, in 1984.
2: 33 Coulomb Functions
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3: Barry I. Schneider
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► in chemistry from Brooklyn College, his M.
… in chemistry from Yale University and a Ph.
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►He has authored or co-authored 140 refereed papers and books and has given numerous invited talks in the US and abroad.
…He also serves as a reviewer for a variety of journals inside and outside the US.
…Recently he has served as Co-Chair of the US government Fast Track Action Committee to update the US strategic computing plan.
4: Possible Errors in DLMF
Possible Errors in DLMF
►We have strived for the utmost in correctness, clarity and accuracy, having validated each chapter with both internal and external experts. … ►There are also cases where browser bugs or poor fonts can be misleading; you can verify MathML display by comparing the to the images or TeXfound under Encodings in the Info boxes (see About MathML). Errors in the printed Handbook may already have been corrected in the online version; please consult Errata. … ►Please contact us.5: Brian Antonishek
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►Brian Antonishek is on the staff of the Visualization and Usability Group in the Information Access Division of the Information Technology Laboratory at the National Institute of Standards and Technology.
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►Antonishek received the Bachelor of Science degree in computer science from the University of Pittsburgh, Johnstown, Pennsylvania, in 1990 and the Master of Science degree in computer science from the University of Pittsburgh, Pittsburgh, Pennsylvania, in 1996.
Before coming to NIST in 1997, he developed user interaction and scientific visualization techniques for viewing and analyzing 3D engineering data.
His research areas include human robot interaction, medical data anlysis, and 3D web interactions using VRML and X3D.
6: 12.16 Mathematical Applications
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►PCFs are used as basic approximating functions in the theory of contour integrals with a coalescing saddle point and an algebraic singularity, and in the theory of differential equations with two coalescing turning points; see §§2.4(vi) and 2.8(vi).
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►In Brazel et al. (1992) exponential asymptotics are considered in connection with an eigenvalue problem involving PCFs.
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►PCFs are also used in integral transforms with respect to the parameter, and inversion formulas exist for kernels containing PCFs.
…Integral transforms and sampling expansions are considered in Jerri (1982).
7: 27.17 Other Applications
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►Reed et al. (1990, pp. 458–470) describes a number-theoretic approach to Fourier analysis (called the arithmetic Fourier transform) that uses the Möbius inversion (27.5.7) to increase efficiency in computing coefficients of Fourier series.
►Congruences are used in constructing perpetual calendars, splicing telephone cables, scheduling round-robin tournaments, devising systematic methods for storing computer files, and generating pseudorandom numbers.
…Apostol and Zuckerman (1951) uses congruences to construct magic squares.
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►There are also applications of number theory in many diverse areas, including physics, biology, chemistry, communications, and art.
Schroeder (2006) describes many of these applications, including the design of concert hall ceilings to scatter sound into broad lateral patterns for improved acoustic quality, precise measurements of delays of radar echoes from Venus and Mercury to confirm one of the relativistic effects predicted by Einstein’s theory of general relativity, and the use of primes in creating artistic graphical designs.
8: Notices
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►As a condition of using the DLMF, you explicitly release NIST from any and all liabilities for any damage of any type that may result from errors or omissions in the DLMF.
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►The DLMF wishes to provide users of special functions with essential reference information related to the use and application of special functions in research, development, and education.
Using special functions in applications often requires computing them.
…We do this in two ways.
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►Please contact us if you have software that you believe should be listed.
9: Bruce R. Miller
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► 1953 in Houston, Texas) is on the staff of the Applied and Computational Mathematics Division of the Information Technology Laboratory in the National Institute of Standards and Technology.
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►D in experimental physics from the University of Texas at Austin in 1983.
…In 1989, he was awarded the Department of Commerce’s Silver Medal for this work.
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►He is the developer of the tools used to process the DLMF into both book and web forms.
In particular, he developed the LaTeXML system used for converting the LaTeX source documents into XML and MathML from which the DLMF website is constructed.
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10: About MathML
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►The DLMF uses MathML Core, a subset designed specifically for browsers.
►The mathematical notations used in DLMF are complex enough that a fairly complete MathML implementation is required.
…However, the MathJax javascript library can also used to render the MathML, albeit more slowly.
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►Of course you are encouraged to use a modern, up-to-date browser.
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►DLMF uses the STIX web font to provide a consistent coverage.
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