All Mathieu functions have the form 
, where 
has period 
and 
is known as the Mathieu characteristic exponent. This exponent
is returned by the Wolfram Language
function MathieuCharacteristicExponent[a,
q].
Mathieu Characteristic Exponent
See also
Mathieu FunctionRelated Wolfram sites
http://functions.wolfram.com/MathieuFunctions/MathieuCharacteristicExponent/Explore with Wolfram|Alpha
References
Alhargan, F. A. "A Complete Method for the Computations of Mathieu Characteristic Functions and Their Characteristic Numbers of Integer Orders." SIAM Rev. 38, 239-255, 1996.Dingle, R. B. and Müller, H. J. W. "Asymptotic Expansions of Mathieu Functions and Their Characteristic Numbers." J. reine angew. Math. 211, 11-32, 1962.Cite this as:
Weisstein, Eric W. "Mathieu Characteristic Exponent." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MathieuCharacteristicExponent.html