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Search Publications by: Howard Cohl (Fed)

Displaying 51 - 61 of 61

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

Eigenfunction expansions for a fundamental solution of Laplace's equation on R 3 in parabolic and elliptic cylinder coordinates

August 14, 2012

Author(s)

Howard S. Cohl, Hans Volkmer

A fundamental solution of Laplace's equation in three dimensions is expanded in harmonic functions that are separated in parabolic or elliptic cylinder coordinates. There are two expansions in each case which reduce to expansions of the Bessel functions J

Fourier and Gegenbauer expansions for a fundamental solution of the Laplacian in the hyperboloid model of hyperbolic geometry

March 23, 2012

Author(s)

Howard S. Cohl, Ernie G. Kalnins

Due to the isotropy of d-dimensional hyperbolic space, there exists a spherically symmetric fundamental solution for its corresponding Laplace-Beltrami operator. The R-radius hyperboloid model of hyperbolic geometry with R > 0 represents a Riemannian

TABLE ERRATA for Magnus, Oberhettinger & Soni (1966): Formulas and Theorems for the Special Functions of Mathematical Physics

February 16, 2012

Author(s)

Howard S. Cohl

A TABLE ERRATA is submitted concerning a formula in terms of a sum of two Gauss hypergeometric functions for Ferrers function of the second kind. This error occurs on p. 167 of Magnus, Oberhettinger & Soni (1966) Formulas and Theorems for the Special

Fundamental Solution of Laplace's Equation in Hyperspherical Geometry

November 29, 2011

Author(s)

Howard S. Cohl

Due to the isotropy of $d$-dimensional hyperspherical space, one expects there to exist a spherically symmetric fundamental solution for its corresponding Laplace-Beltrami operator. The $R$-radius hypersphere ${\mathbf S}_R^d$ with $R>0$, represents a

On Parameter Differentiation for Integral Representations of Associated Legendre Functions

May 24, 2011

Author(s)

Howard S. Cohl

For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated