Mathieu function
In mathematics, Mathieu functions, sometimes called angular Mathieu functions, are solutions of Mathieu's differential equation d 2 y d x 2 + ( a − 2 q cos ( 2 x ) ) y = 0 , {\displaystyle {\frac {d^{2}y}{dx^{2}}}+(a-2q\cos(2x))y=0,} where a, q are real-valued parameters. Since we may add π/2 to x to change the sign of q, it is a usual convention to set q ≥ 0.