We construct a one-parameter family of generalized Mathieu functions, which are reduced
quaternion-valued functions of a pair of real variables lying in an ellipse, and which we call λ …

In this paper we consider the 2D time–harmonic Maxwell equations in elliptic coordinates
through certain quaternionic perturbed Dirac operator. The main goal is aimed to analyze an …

A theory of quaternion-valued functions, called hyperholomorphic, of two real variables has
long been established. This theory is in the same relation to the two dimensional Helmholtz …

The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for
different classes of functions and curves, is still widely used in mathematical physics and …

In the last few years considerable attention has been paid to the role of the prolate
spheroidal wave functions (PSWFs) to many practical signal and image processing …

This study aims to study a class of Dirichlet-type problems associated with the two-
dimensional Helmholtz equation with complex potential. Orthogonal decompositions of the …

The scalar spherical wave functions (SWFs) are solutions to the scalar Helmholtz equation
obtained by the method of separation of variables in spherical polar coordinates. These …

On the 2D Quaternionic Metaharmonic Layer Potentials Page 1 Mediterr. J. Math. (2017) 14:195
DOI 10.1007/s00009-017-0995-6 1660-5446/17/050001-18 published online August 31, 2017 …

Over the past few years, considerable attention has been given to the role played by the
Lamé's Wave Functions (LWFs) in various problems of mathematical physics and …

We construct a set of quaternionic metamonogenic functions (that is, in Ker (D+ λ) for diverse
real λ) in the unit disk, such that every metamonogenic function is approximable in the …