Mathieu functions

• Mathieu functions
  • Overview — An overview of the Mathieu Functions toolbox.
  • mathieu_Arm — Compute expansion coefficients 'Arm' and eigenvalue 'am' for even angular and radial Mathieu functions.
  • mathieu_Brm — Compute expansion coefficients 'Brm' and eigenvalue 'bm' for odd angular and radial Mathieu functions.
  • mathieu_ang_ce — Compute even angular Mathieu function 'ce' or its first derivative.
  • mathieu_ang_se — Compute odd angular Mathieu function 'se' or its first derivative.
  • mathieu_cart2ell — Converts from Cartesian coordinates to elliptical coordinates.
  • mathieu_cart2pol — Transform from Cartesian to polar (cylindrical) coordinates.
  • mathieu_ell2cart — Converts from elliptical to Cartesian coordinates.
  • mathieu_ell_in_pol — Calculates polar coordinates of a point at angle (theta) on ellipse.
  • mathieu_mathieu — Evaluates periodic Mathieu functions.
  • mathieu_mathieuS — Evaluates the solution to first kind of Mathieu Equation.
  • mathieu_mathieuexp — Evaluates the characteristic exponent.
  • mathieu_mathieuf — Evaluates characteristic values and expansion coefficients.
  • mathieu_membrane_mode — Calculate elliptical membrane mode for known semi-axes, mode numbers, mode type and boundary condition (Soft/Dirichlet or Hard/Neumann).
  • mathieu_pol2cart — Transform from polar (or cylindrical) coordinates to Cartesian.
  • mathieu_rad_ce — Compute even radial (modified) Mathieu function of the first kind 'Ce' or its first derivative.
  • mathieu_rad_fey — Compute even radial (modified) Mathieu function of the second kind 'Fey' or its first derivative.
  • mathieu_rad_gey — Compute odd radial (modified) Mathieu function of the second kind 'Gey' or its first derivative.
  • mathieu_rad_mc — Compute even radial (modified) Mathieu function 'Mc' or its first derivative (kinds 1 and 2).
  • mathieu_rad_ms — Compute odd radial (modified) Mathieu function 'Ms' or its first derivative (kinds 1 and 2).
  • mathieu_rad_se — Compute odd radial (modified) Mathieu function of the first kind 'Se' or its first derivative.
  • mathieu_rootfinder — Rootfinder for radial Mathieu function or its first derivative (finds q values of given radial function type with known order m and radial argument ξ0, which satisfies the equation RMF_m(q,xi0) = 0 (Dirichlet boundary condition) or RMF_m'(q,xi0) = 0 (Neumann boundary condition).