Mathieu Functions

  title={Mathieu Functions},
  author={Elwyn T. Whittaker and George Neville Watson},
  journal={A Course of Modern Analysis},

Computation and Applications of Mathieu Functions: A Historical Perspective

This paper surveys and recapitulates the historical development of the theory and methods of computation for Mathieu functions and modified Mathieu function and identifies some gaps in current software capability, particularly to do with double eigenvalues of the Mathieu equation.

Reduced-quaternionic Mathieu functions, time-dependent Moisil-Teodorescu operators, and the imaginary-time wave equation

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-reduced

Entropic analysis of optomechanical entanglement for a nanomechanical resonator coupled to an optical cavity field

  • J. Choi
  • Physics
    SciPost Physics Core
  • 2021
We investigate entanglement dynamics for a nanomechanical resonator coupled to an optical cavity field through the analysis of the associated entanglement entropies. The effects of time variation of

Discrete Bessel and Mathieu Functions

The two-dimensional Helmholtz equation separates in elliptic coordinates based on two distinct foci, a limit case of which includes polar coordinate systems when the two foci coalesce. This equation

A Compact, Passive Frequency-Hopping Harmonic Sensor Based on a Microfluidic Reconfigurable Dual-Band Antenna

It is demonstrated that the type of liquid mixture filling in the fluidic cavity can be clearly perceived by reading the peak received signal strength indicator (RSSI) in the spectrum of second harmonics.

Analytic baby skyrmions at finite density

We introduce a consistent ansatz for the baby Skyrme model in (2+1)-dimensions which is able to reduce the complete set of field equations to just one equation for the profile function in situations

Metric preheating and radiative decay in single-field inflation

At the end of inflation, the inflaton oscillates at the bottom of its potential and these oscillations trigger a parametric instability for scalar fluctuations with wavelength λ comprised in the

Almost Exact Computation of Eigenvalues in Approximate Differential Problems

This work presents a method for eigenvalues computation following the Tau method philosophy and using Tau Toolbox tools, allowing for high accuracy approximations of differential eigen values.