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SciPy Reference Guide, Release 0.8.dev
mathieu_a
lmbda=mathieu_a(m,q) returns the characteristic value for the even solution, ce_m(z,q), of Mathieu’s equation
mathieu_b
lmbda=mathieu_b(m,q) returns the characteristic value for the odd solution, se_m(z,q), of Mathieu’s equation
These are not universal functions:
mathieu_even_coef(m, q) Compute expansion coefficients for even mathieu functions and
mathieu_odd_coef(m, q) Compute expansion coefficients for even mathieu functions and
mathieu_even_coef(m, q)
Compute expansion coefficients for even mathieu functions and modified mathieu functions.
mathieu_odd_coef(m, q)
Compute expansion coefficients for even mathieu functions and modified mathieu functions.
The following return both function and first derivative:
mathieu_cem(x1, x2, out1) (y,yp)=mathieu_cem(m,q,x) returns the even Mathieu function, ce_m(x,q),
mathieu_sem(x1, x2, out1) (y,yp)=mathieu_sem(m,q,x) returns the odd Mathieu function, se_m(x,q),
mathieu_modcem1(x1, x2, out1) (y,yp)=mathieu_modcem1(m,q,x) evaluates the even modified Matheiu function
mathieu_modcem2(x1, x2, out1) (y,yp)=mathieu_modcem2(m,q,x) evaluates the even modified Matheiu function
mathieu_modsem1(x1, x2, out1) (y,yp)=mathieu_modsem1(m,q,x) evaluates the odd modified Matheiu function
mathieu_modsem2(x1, x2, out1) (y,yp)=mathieu_modsem2(m,q,x) evaluates the odd modified Matheiu function
mathieu_cem
(y,yp)=mathieu_cem(m,q,x) returns the even Mathieu function, ce_m(x,q), of order m and parameter q evaluated
at x (given in degrees). Also returns the derivative with respect to x of ce_m(x,q)
mathieu_sem
(y,yp)=mathieu_sem(m,q,x) returns the odd Mathieu function, se_m(x,q), of order m and parameter q evaluated
at x (given in degrees). Also returns the derivative with respect to x of se_m(x,q).
mathieu_modcem1
(y,yp)=mathieu_modcem1(m,q,x) evaluates the even modified Matheiu function of the first kind, Mc1m(x,q),
and its derivative at x for order m and parameter q.
mathieu_modcem2
(y,yp)=mathieu_modcem2(m,q,x) evaluates the even modified Matheiu function of the second kind, Mc2m(x,q),
and its derivative at x (given in degrees) for order m and parameter q.
mathieu_modsem1
(y,yp)=mathieu_modsem1(m,q,x) evaluates the odd modified Matheiu function of the first kind, Ms1m(x,q),
and its derivative at x (given in degrees) for order m and parameter q.
mathieu_modsem2
(y,yp)=mathieu_modsem2(m,q,x) evaluates the odd modified Matheiu function of the second kind, Ms2m(x,q),
and its derivative at x (given in degrees) for order m and parameter q.
440 Chapter 3. Reference