11 citations · 62 across the 21 of their papers we have counts for
24 papers
The Laplace-Beltrami Operator on the Surface of the Ellipsoid
Hans Volkmer
The Laplace-Beltrami operator on (the surface of) a triaxial ellipsoid admits a sequence of real eigenvalues diverging to plus infinity. By introducing ellipsoidal coordinates, thi…
On the Hill Discriminant of Lamé's Differential Equation
Hans Volkmer
Lamé's differential equation is a linear differential equation of the second order with a periodic coefficient involving the Jacobian elliptic function depending on the…
Internal and external harmonics in bi-cyclide coordinates
Brandon Alexander, Howard S. Cohl, Hans Volkmer
The Laplace equation in three dimensional Euclidean space is -separable in bi-cyclide coordinates leading to harmonic functions expressed in terms of Lamé-Wangerin functions cal…
Peanut harmonic expansion for a fundamental solution of Laplace's equation in flat-ring coordinates
Lijuan Bi, Howard S. Cohl, Hans Volkmer
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 o…
Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates
Lijuan Bi, Howard S. Cohl, Hans Volkmer
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 produc…
Fourier series representation of Ferrers function P
Hans Volkmer
In this note we consider the Fourier expansion of the Ferrers function P of the first kind. We determine its mode of convergence.
Geometric Brownian motion with affine drift and its time-integral
Runhuan Feng, Pingping Jiang, Hans Volkmer
The joint distribution of a geometric Brownian motion and its time-integral was derived in a seminal paper by Yor (1992) using Lamperti's transformation, leading to explicit soluti…
Gauss Hypergeometric Representations of the Ferrers Function of the Second Kind
Howard S. Cohl, Justin Park, Hans Volkmer
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 hyperge…
1-Wasserstein Distance on the Standard Simplex
Andrew Frohmader, Hans Volkmer
Wasserstein distances provide a metric on a space of probability measures. We consider the space of all probability measures on the finite set where is…
Eigenvalue Problems for Lamé's Differential Equation
Hans Volkmer
The Floquet eigenvalue problem and a generalized form of the Wangerin eigenvalue problem for Lamé's differential equation are discussed. Results include comparison theorems for eig…
On transfer operators on the circle with trigonometric weights
Xianghong Chen, Hans Volkmer
We study spectral properties of the transfer operators defined on the circle by $$(Lu)(t)=\frac{1}{d}\sum_{i=0}^{d-1} f\left(\frac{t+i}{d}\right…
The modulus of Whittaker functions
Hans Volkmer
The paper discusses some properties of the modulus of the Whittaker function . In particular, completely monotone functions expressed in terms of $|W_{k,…
Convergence of Magnus integral addition theorems for confluent hypergeometric functions
Howard S. Cohl, Jessie Hirtenstein, Hans Volkmer
In 1946, Magnus presented an addition theorem for the confluent hypergeometric function of the second kind with argument expressed as an integral of a product of two '…
The Asymptotic Expansion of Kummer Functions for Large Values of the -Parameter, and Remarks on a Paper by Olver
Hans Volkmer
It is shown that a known asymptotic expansion of the Kummer function as tends to infinity is valid for on the full Riemann surface of the logarithm. A correspond…
Conditional Asian Options
Runhuan Feng, Hans W. Volkmer
Conditional Asian options are recent market innovations, which offer cheaper and long-dated alternatives to regular Asian options. In contrast with payoffs from regular Asian optio…
Generalizations of generating functions for higher continuous hypergeometric orthogonal polynomials in the Askey scheme
Michael A. Baeder, Howard S. Cohl, Hans Volkmer
We use connection relations and series rearrangement to generalize generating functions for several higher continuous orthogonal polynomials in the Askey scheme, namely the Wilson,…
Expansions for a fundamental solution of Laplace's equation on in 5-cyclidic harmonics
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…
An identity of hitting times and its application to the valuation of guaranteed minimum withdrawal benefit
Runhuan Feng, Hans W. Volkmer
In this paper we explore an identity in distribution of hitting times of a finite variation process (Yor's process) and a diffusion process (geometric Brownian motion with affine d…
Analytic Solutions for D-optimal Factorial Designs under Generalized Linear Models
Liping Tong, Hans W. Volkmer, Jie Yang
We develop two analytic approaches to solve D-optimal approximate designs under generalized linear models. The first approach provides analytic D-optimal allocations for generalize…
Generalizations of generating functions for hypergeometric orthogonal polynomials with definite integrals
Howard S. Cohl, Connor MacKenzie, Hans Volkmer
We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating funct…
Separation of variables in an asymmetric cyclidic coordinate system
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 coordinat…
Eigenfunction expansions for a fundamental solution of Laplace's equation on in parabolic and elliptic cylinder coordinates
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 e…
Optimal Dividend Payments for the Piecewise-Deterministic Poisson Risk Model
Runhuan Feng, Hans Volkmer, Shuaiqi Zhang +1
This paper considers the optimal dividend payment problem in piecewise-deterministic compound Poisson risk models. The objective is to maximize the expected discounted dividend pay…
Generalized Ellipsoidal and Sphero-Conal Harmonics
Hans Volkmer
Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of the Laplace equation that can be expressed in terms of Lame polynomials. Generalized ellipsoidal and sp…