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Search Publications by: Howard Cohl (Fed)

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Displaying 1 - 25 of 61

Multi-integral representations for Jacobi functions of the first and second kind

October 5, 2023
Author(s)
Howard Cohl, Roberto S. Costas-Santos
One may consider the generalization of Jacobi polynomials and the Jacobi func- tion of the second kind to a general function where the index is allowed to be a complex number instead of a non-negative integer. These functions are referred to as Jacobi func

Internal and external harmonics in bi-cyclide coordinates

July 20, 2023
Author(s)
Hans Volkmer, Brandon Alexander, Howard Cohl
The Laplace equation in three-dimensional Euclidean space is R-separable in bi-cyclide coordinates leading to harmonic functions expressed in terms of Lamé–Wangerin functions called internal and external bi-cyclide harmonics. An expansion for a fundamental

Discovery and Recognition of Formula Conceptsusing Machine Learning

July 13, 2023
Author(s)
Howard Cohl, Bela Gipp, Moritz Schubotz, Philipp Scharpf
Citation-based Information Retrieval (IR) methods for scientific documents have proven effective for IR applications, such as Plagiarism Detection or Literature Recommender Systems in academic disciplines that use many references. In science, technology

Gauss Hypergeometric Representations of the Ferrers Function of the Second Kind

May 20, 2021
Author(s)
Howard Cohl, Hans Volkmer, Justin Park
We derive all eighteen Gauss hypergeometric representations for the Ferrers function of the second kind, each with a different argument. They are obtained from the eighteen hypergeometric representations of the associated Legendre function of the second

Discovering Mathematical Objects of Interest - A Study of Mathematical Notations

April 1, 2020
Author(s)
Howard S. Cohl, Andre Greiner Petter, Moritz Schubotz, Corinna Breitinger, Fabian Muller, Akiko Aizawa, Bela Gipp
Mathematical notation, i.e., the writing system used to communicate concepts in mathematics, encodes valuable information for a variety of information search and retrieval systems. Yet, mathematical notations remain mostly unutilized by today's systems. In

Towards Formula Concept Discovery and Recognition

July 25, 2019
Author(s)
Howard S. Cohl, Philipp Scharpf, Moritz Schubotz, Bela Gipp
Citation-based Information Retrieval (IR) methods for scientific documents have proven to be effective in academic disciplines that use many references. In science, technology, engineering, and mathematics (STEM), researchers cite less often but employ

On a generalization of the Rogers generating function

July 14, 2019
Author(s)
Howard Cohl, Roberto Costas-Santos, Tanay Wakhare
We derive a generalized Rogers generating function and corresponding definite integral, for the continuous q-ultraspherical polynomials by applying its connection relation and utilizing orthogonality. Using a recent generalization of the Rogers generating

Some generating functions for q-polynomials

December 15, 2018
Author(s)
Howard Cohl, Roberto Costas-Santos, Tanay Wakhare
We obtain $q$-analogues of the Sylvester, Cesaro, Pasternack, and Bateman polynomials. We also derive generating functions for these polynomials.

MathTools: An Open API for Convenient MathML Handling

July 18, 2018
Author(s)
Howard S. Cohl, Andre Greiner Petter, Moritz Schubotz, Bela Gipp
Mathematical formulae carry complex and essential semantic in- formation in a variety of formats. Accessing this information with different sys- tems requires a standardized machine-readable format that is capable of encod- ing presentational and semantic