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I have the following function to evaluate in a power series:

[tex]

f(a)=\frac{\pi}{8d}\frac{1}{\left (\sinh \left ( \frac{\pi a}{2 d} \right) \right)^2}

[/tex]

Maple computes then following

[tex]

f(a) = \frac{\pi}{8d} \left ( \frac{4 d^2}{\pi^2 a^2} - \frac{1}{3} + O(a^2) \right)

[/tex]

When I ask Maple if this series is of Taylor or Laurent type it tells me that it is neither. I tried to compute the Taylor series around [itex]a=0[/itex] but I get stuck at the first term, namely [itex]f(0)[/itex], which is infinite. The first term of the expression obtained by Maple is precisely equal to the inverse of the first non-zero term of the Taylor series of

[tex]

g(a)= \left (\sinh \left ( \frac{\pi a}{2 d} \right) \right)^2 = \left (0 + \frac{\pi a}{2 d} +\right )^2 = \frac{\pi^2 a^2}{4 d^2}

[/tex]

But I can't figure out where do the other terms come from. Anyone knows how does Maple evaluate this series?

Any help greatly appreciated

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# Homework Help: Series of hyperbolic function

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