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Power series for the tangent
The tangent can be expresseed by the power series
Explanation
The derivatives of the tangent are
In the point x = 0 applies tan (0) = 0 so
We substitute this in the Taylor series and find
zodat
of anders geschreven
General format
You can write the power series as a sum
where Un isthe n-th up/down number. Or
where Bn is the n-th Bernoulli number.
Example 1
You can see that tan (0) = 0, because according to the formula applies
tan (0) = 0 + 0 + 0 + ... = 0