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Power series for the hyperbolic tangent
The hyperbolische tangent has the power series
Explanation
De afgeleiden zijn
⁽⁵⁾ = 16 tanh x − 136 tanh³ x.gif){kind=small}
The point x = 0 gives tanh (0) = 0 so
We substitute this in the Taylor series and find
zodat
Example 1
You can see that tanh (0) = 0, because
tanh (0) = 0 − 0 + 0 − 0 + ⋯ = 0