[SciPy-User] Understanding parameters of scipy.special Mathieu_cem function etc.

[Warren Weckesser]

On Wed, Jul 26, 2017 at 5:52 AM, Austin Tobin <austin.tobin at gmail.com>
wrote:

> I am trying to relate the Mathieu equation found in Wikipedia Mathieu
> Equation <https://en.wikipedia.org/wiki/Mathieu_function/> to the one
> implemented in scipy.special. In Wikipedia there are 3 inputs, a,q and the
> parameter along which the integration proceeds.
>
> mathieu_cem takes three inputs, an order (integer), a characteristic
> parameter and the the parameter along which the integration proceeds in
> degrees. I am trying to relate a and q to the order and characteristic
> parameter.
>

In the Mathieu equation, 'a' is an arbitrary parameter.  However, for a
given 'q', there is only a discrete set of values of 'a' for which the
equation has even periodic solutions.  Call these a_0(q), a_1(q), a_2(q),
etc.  'mathieu_a(m, q)' computes a_m(q), and 'mathieu_cem(m, q, x)' is the
even periodic solution associated with a_m(q).

Warren


If it helps I am trying to simulate a quadrupole mass spectrometer with a
> and q being trapping parameters.
> Regards,
> Austin
>
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