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For small values of q, these functions do resemble sine and cosine near the origin. In the example plotted below (same values of a,q as above), the Mathieu cosine is plotted in red and cosine in green:
[[Image:MathieuCosine_example.gif|center]]
For this example, the [[McLaurin series]] is
:<math>C(1,1/5,x) = 1 - \frac{3}{10} \, x^2 - \frac{31}{600} \, x^4 + \frac{1613}{9000} \, x^6 + O(x^8)</math>
==Periodic solutions==
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