Mathieu Function

Mathieu Function

In mathematics, the Mathieu functions are certain special functions useful for treating a variety of problems in applied mathematics, including:

• vibrating elliptical drumheads,
• quadrupoles mass filters and quadrupole ion traps for mass spectrometry
• wave motion in periodic media, such as ultracold atoms in an optical lattice
• the phenomenon of parametric resonance in forced oscillators,
• exact plane wave solutions in general relativity,
• the Stark effect for a rotating electric dipole,
• in general, the solution of differential equations that are separable in elliptic cylindrical coordinates.

They were introduced by Émile Léonard Mathieu (1868) in the context of the first problem.