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Hyperbolic cosine

The hyperbolic cosine can be expressed with exponential functions as

 


Explanation

In the power series for the hyperbolic cosine are only even exponents and all terms have a plus sign

After duplicating all terms you get

To this we add odd exponents and subtract these immediately

Rearranging gives

In brackets are two power series for exponential functions which means

so that

 


Example 1

You can see that cosh (0) = 1, because

 


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