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How can I derive the Taylor series expansion and the radius of convergence for hyperbolic tangent tanh(x) around the point x=0.

I can find the expression for the above in various sites, but the proof is'nt discussed. I guess the above question reduces to how can I get the expression for the n^th order derivative of tanh(x) in terms of Bernoulli numbers.

Many thanks in advance.

joel.

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# Taylor series for tanh

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