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Search Publications by: Howard Cohl (Fed)

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Displaying 26 - 50 of 61

The orthogonality of Al-Salam-Carlitz polynomials for complex parameters

January 31, 2018
Author(s)
Howard Cohl, Wenqing Xu, Roberto Costas-Santos
In this contribution, we study the orthogonality conditions satisfied by Al-Salam-Carlitz polynomials $U^(a)}_n(x;q)$ when the parameters $a$ and $q$ are not necessarily real nor 'classical'. We establish orthogonality on a simple contour in the complex

The power collection method for connection relations: Meixner polynomials

November 7, 2017
Author(s)
Howard Cohl, Michael Baeder, Roberto Costas-Santos, Wenqing Xu
We use and derive connection and connection-type relations for Meixner and Krawtchouk polynomials. These relations are used to derive generalizations of generating functions for these orthogonal polynomials. The coefficients of these generalized generating

VMEXT: A Visualization Tool for Mathematical Expression Trees

July 12, 2017
Author(s)
Moritz Schubotz, Howard Cohl, Bela Gipp, Norman Meuschke, Thomas Hepp
Mathematical expressions can be represented as a tree consisting of terminal symbols, such as identifiers or numbers (leaf nodes), and functions or operators (non-leaf nodes). Expression trees are an important concept to store and process mathematical

Sampling Architectures for Ultra-Wideband Signals

July 3, 2017
Author(s)
Howard S. Cohl, Steve Casey
Ultra-wideband (UWB) signal processing is a technology with many features that could develop into advances in communication and information technology. The technology has tremendous potential, but also presents challenges to the signal processing community

Semantic Preserving Bijective Mappings of Mathematical Formulae between Word Processors and Computer Algebra Systems

June 28, 2017
Author(s)
Howard S. Cohl, Bonita V. Saunders, Marjorie A. McClain, Moritz Schubotz, Joon Bang, Juergen Gerhardt, Andre Greiner Petter
There are many different approaches to represent mathematical expressions on computers. Word processors like LaTeX offer the ability to render mathematical expressions as one would write these on paper. Using LaTeX, LaTeXML, and tools generated for use in

Getting the units right

July 25, 2016
Author(s)
Howard S. Cohl, Moritz A. Schubotz, David Veenhuis
To understand applied physics, and physical formulae in particular, the investigation of identifier units is beneficial. However, normally the units are not given explicitly in formulae and have to be inferred. In this paper, we investigate how this

Report from Open Problems Session at OPSFA-13

July 21, 2016
Author(s)
Howard S. Cohl, Richard Askey, Rick Beatson, Charles Dunkl, Christoph Koutschan, Sheehan Olver, Yuan Xu, Wolfgang Zu Castell, Wadim Zudilin, Ted Chihara
We provide the open problems presented at OPSFA-13, Gaithersburg, Maryland, June 4, 2015. Howard Cohl, National Institute of Standards and Technology, has collected these open problems.

Semantification of Identifiers in Mathematics for Better Math Information Retrieval

July 17, 2016
Author(s)
Moritz Schubotz, Alexey Grigoriev, Howard Cohl, Norman Meushke, Bela Gipp, Volker Markl
Mathematical formulae are essential in science, but face challenges of ambiguity, due to the use of a small number of identifiers to represent an immense number of concepts. Corresponding to word sense disambiguation in Natural Language Processing, we

Some dual definite integrals for Bessel functions

September 24, 2015
Author(s)
Howard S. Cohl, Rebekah M. Palmer, Sean Nair
Based on known definite integrals of Bessel functions of the first kind, we obtain exact solutions to unknown definite integrals using the method of integral transforms from Hankel's transform.

Digital Repository of Mathematical Formulae KLS Seeding Project

June 23, 2015
Author(s)
Howard S. Cohl, Marjorie A. McClain, Bonita V. Saunders, Moritz Schubotz, Cherry Y. Zou, Alex A. Danoff, Azeem S. Mohammed
One initial goal for the DRMF is to seed our digital compendium with fundamental orthogonal polynomial formulae. We have received permission from Springer-Verlag and the authors to use formulae from Chapters 1, 9, and 14 from the book "Hypergeometric

UWB Signal Processing: Projection, B-Splines, and Modified Gegenbauer Bases

May 25, 2015
Author(s)
Howard S. Cohl, Stephen D. Casey
Ultra-wide band (UWB) systems require either rapidly changing or very high sampling rates. Conventional analog-to-digital devices have limited dynamic range. We investigate UWB signal processing via a basis projection method and a basis system designed for

Digital Repository of Mathematical Formulae

October 17, 2014
Author(s)
Howard S. Cohl, Marjorie A. McClain, Bonita V. Saunders, Moritz Schubotz, Janelle Williams
The purpose of the NIST Digital Repository of Mathematical Formulae (DRMF) is to create a digital compendium of mathematical formulae for orthogonal polynomials and special functions (OPSF) and of associated mathematical data. The DRMF addresses needs of

Separation of variables in an asymmetric cyclidic coordinate system

June 27, 2013
Author(s)
Howard S. Cohl, Hans Volkmer
A global analysis is presented of solutions for Laplace's equation on three-dimensional Euclidean space in one of the most general orthogonal asymmetric confocal cyclidic coordinate system which admits solutions through separation of variables. We refer to