Publications

Displaying 1 - 25 of 111

The Digital Shadow of Mathematics and its Ramifications

June 17, 2024

Author(s)

Howard Cohl, Moritz Schubotz

A description of the ongoing effort and status of mathematical semantics in the digital age.

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 Concepts Using 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

Nonterminating transformations and summations associated with some q-Mellin-Barnes integrals

March 1, 2023

Author(s)

Howard Cohl, Roberto Costas-Santos

In many cases one may encounter an integral which is of $q$-Mellin--Barnes type. These integrals are easily evaluated using theorems which have a long history dating back to Slater, Askey, Gasper, Rahman and others. We derive some interesting $q$-Mellin-

Two-dimensional contiguous relations for linearization coefficients of orthogonal polynomials in the Askey-scheme

February 10, 2023

Author(s)

Howard Cohl, Lisa Ritter

By using the three-term recurrence relation for orthogonal polynomials, we produce a collection of two-dimensional contiguous relations for certain generalized hypergeometric functions. These generalized hypergeometric functions arise through linearization

Generalizations of generating functions for basic hypergeometric orthogonal polynomials

November 19, 2022

Author(s)

Howard Cohl, Philbert Hwang, Roberto S. Costas-Santos

We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one extra free parameter to them. In particular, we generalize generating functions for the continuous q-ultraspherical/Rogers

Symmetry of terminating basic hypergeometric series representations of the Askey-Wilson polynomials

August 10, 2022

Author(s)

Howard Cohl, Roberto S. Costas-Santos

In this paper, we explore the symmetric nature of the terminating basic hypergeometric series representations of the Askey–Wilson polynomials and the corresponding terminating basic hypergeometric transformations that these polynomials satisfy. In

Gegenbauer expansions and addition theorems for a binomial and logarithmic fundamental solution of the even-dimensional Euclidean polyharmonic equation

August 4, 2022

Author(s)

Howard Cohl, James F. Lawrence, Lisa Ritter, Jessie Hirtenstein

On even-dimensional Euclidean space for integer powers of the positive Laplace operator greater than or equal to half the dimension, a fundamental solution of the polyharmonic equation has binomial and logarithmic behavior. Gegenbauer polynomial expansions

Utility of integral representations for basic hypergeometric functions and orthogonal polynomials

June 23, 2022

Author(s)

Roberto S. Costas-Santos, Howard Cohl

We describe the utility of integral representations for sums of basic hypergeometric functions. In particular we use these to derive an infinite sequence of transformations for symmetrizations over certain variables which the functions possess. These

Expansion for a fundamental solution of Laplace's equation in flat-ring cyclide coordinates

June 3, 2022

Author(s)

Howard Cohl, Hans Volkmer, Lijuan Bi

We derive an expansion for the fundamental solution of Laplace's equation in flat-ring coordinates in three-dimensional Euclidean space. This expansion is a double series of products of functions that are harmonic in the interior and exterior of "flat

Peanut Harmonic Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Coordinates

April 21, 2022

Author(s)

Hans Volkmer, Lijuan Bi, Howard Cohl

We derive an expansion for the fundamental solution of Laplace's equation in flat-ring cyclide coordinates in three-dimensional Euclidean space. This expansion is a double series of products of functions that are harmonic in the interior and exterior of

Comparative Verification & Validation of Digital Mathematical Libraries and Computer Algebra Systems

March 30, 2022

Author(s)

Howard Cohl, Abdou Youssef, Andre Greiner Petter, Moritz Schubotz, Bela Gipp, Akiko Aizawa, Avi Trost, Rajen Dey

Digital Mathematical Libraries assemble the knowledge of years of mathematical research. Numerous disciplines (e.g., physics, engineering, pure and applied mathematics) rely heavily on compendia gathered findings. Likewise, modern research relies more and

On the relation between Gegenbauer polynomials and the Ferrers function of the first kind

March 30, 2022

Author(s)

Roberto S. Costas-Santos, Howard Cohl

Using the direct relation between the Gegenbauer polynomials C_n^λ(x) and the Ferrers function of the first kind P_μ^ν(x), we compute interrelations between certain Jacobi polynomials, Meixner polynomials, and Ferrers functions of the first and second kind

Connecting Islands: Bridging zbMATH and DLMF with Scholix, a blueprint for connecting expert knowledge systems

June 30, 2021

Author(s)

Moritz Schubotz, Olaf Teschke, Howard Cohl

This paper reports on the recently launched zbMATH Links API. We discuss its potential based on the initial link partner, the National Institute of Standards and Technology Digital Library of Mathematical Functions. As the API provides machine readable

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

Multi-Integral Representations for Associated Legendre and Ferrers Functions

September 25, 2020

Author(s)

Howard S. Cohl

We obtain antiderivatives and complex integral representations for associated Legendre functions and Ferrers functions (associated Legendre functions on-the-cut) of the first and second kind with degree and order equal to within a sign.

Terminating basic hypergeometric representations and transformations for the Askey-Wilson polynomials

August 3, 2020

Author(s)

Howard S. Cohl, Roberto Costas-Santos, Linus Ge

In this survey paper, we exhaustively explore the terminating basic hypergeometric representations of the Askey-Wilson polynomials and the corresponding terminating basic hypergeometric transformations that these polynomials satisfy. From the terminating

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

Terminating basic hypergeometric representations, transformations and summations for the symmetric and q-inverse symmetric subfamilies of the Askey-Wilson polynomials

March 8, 2020

Author(s)

Howard Cohl, Roberto S. Costas-Santos, Linus Ge

In this survey paper, we exhaustively explore the terminating basic hypergeometric representations of the Askey–Wilson polynomials and the corresponding terminating basic hypergeometric transformations that these polynomials satisfy.

Search Publications by: Howard Cohl (Fed)