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Power series for the hyperbolic cosine
The hyperbolic cosine can be expressed as a power series
Explanation
As the hyperbolic cosine can be differentiated continuously, you get
The point x = 0 gives cosh (0) = 1 and sinh (0) = 0, so
We substitute this in the Taylor series and find
The formula contains only even numbers.
Example 1
You can see that cosh (0) = 1, because
cosh (0) = 1 + 0 + 0 + ... = 1