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Search Publications by: Howard Cohl ()

Displaying 76 - 100 of 111

Generalizations of generating functions for higher continuous hypergeometric orthogonal polynomials in the Askey scheme

February 9, 2015

Author(s)

Howard S. Cohl, Hans Volkmer, Michael Baeder

We use connection relations and series rearrangement to generalize generating functions for several higher continuous orthogonal polynomials in the Askey scheme, namely the Wilson, continuous dual Hahn, continuous Hahn, and Meixner-Pollaczek polynomials

Measurement and Analysis of the Lowest Resonant Mode of a Spherical Annular-Sector Patch Antenna

January 29, 2015

Author(s)

Howard S. Cohl

The cavity model for patch antennas has been used extensively since the 1970s. This model gives excellent first order estimates for the antenna's internal fields near any resonant frequency. While frequently used for planar geometries, there is no reason

Evaluation of Similarity-Measure Factors for Formulae based on the NTCIR-11 Math Task

December 9, 2014

Author(s)

Abdou Youssef, Moritz Schubotz, Jimmy Li, Volker Markl, Howard Cohl

In this paper we evaluate different similarity-measure factors for formulae, based on the results of the NTCIR-11 dataset.

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

Expansions for a fundamental solution of Laplace's equation on R 3 in 5-cyclidic harmonics

October 14, 2014

Author(s)

Howard S. Cohl, Hans Volkmer

We derive eigenfunction expansions for a fundamental solution of Laplace's equation in three-dimensional Euclidean space in 5-cyclidic coordinates. There are three such expansions in terms of internal and external 5-cyclidic harmonics of first, second and

Generalization and specializations of generating functions for Jacobi, Gegenbauer, Chebyshev and Legendre polynomials with definite integrals

January 15, 2014

Author(s)

Howard S. Cohl, Connor M. MacKenzie

In this paper we generalize and specialize generating functions for classical orthogonal polynomials, namely Jacobi, Gegenbauer, Chebyshev and Legendre polynomials. We derive a generalization of the generating function for Gegenbauer polynomials through

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

Fourier, Gegenbauer and Jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems

June 5, 2013

Author(s)

Howard S. Cohl

We develop complex Jacobi, Gegenbauer and Chebyshev polynomial expansions for the kernels associated with power-law fundamental solutions of the polyharmonic equation on d-dimensional Euclidean space. From these series representations we derive Fourier

Generalizations of generating functions for hypergeometric orthogonal polynomials with definite integrals

April 30, 2013

Author(s)

Howard S. Cohl, Connor M. MacKenzie

We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating functions are accomplished through series rearrangement using connection

On a generalization of the generating function for Gegenbauer polynomials

January 28, 2013

Author(s)

Howard S. Cohl

We derive a Gegenbauer polynomial expansion for complex powers of the distance between two points in $d$-dimensional Euclidean space. The argument of the Gegenbauer polynomial in the expansion is given by the cosine of the separation angle between the two

Definite integrals using orthogonality and integral transforms

October 19, 2012

Author(s)

Howard S. Cohl, Hans Volkmer

We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.

Erratum: "Developments in determining the gravitational potential using toroidal functions"

October 2, 2012

Author(s)

Howard S. Cohl

We fix several errors in "Developments in determining the gravitational potential using toroidal functions" (Astronomische Nachrichten, Vol. 321, Issue 5/6, p. 363).

Fourier Expansions for a Logarithmic Fundamental Solution of the Polyharmonic Equation

September 28, 2012

Author(s)

Howard S. Cohl

In even-dimensional Euclidean space for integer powers of the Laplacian greater than or equal to the dimension divided by two, a fundamental solution for the polyharmonic equation has logarithmic behavior. We give two approaches for developing a Fourier