1303.0820 (Yoon Seok Choun)
Yoon Seok Choun
We consider the power series expansion of Mathieu function and its integral forms applying three term recurrence formula by Choun. The Mathieu functions are certain special functions useful for treating a variety of problems in applied mathematical physics, including: the phenomenon of parametric resonance in forced oscillators, exact plane wave solutions in general relativity, elliptic membranes and electromagnetic waves, in general, the solution of differential equations that are separable in elliptic cylindrical coordinates. Surprisingly, Mathieu function can be described as Hypergeometric function(Modiefied Bessel function) in its integral forms analytically. In this article, we show exact analytic solution of Mathieu function very precisely in an arrogant way and can be transformed to other well-known special function by using integral forms of it, will be published soon.
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http://arxiv.org/abs/1303.0820
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