These expressions are analogous to the expressions for sine and cosine, depending on Euler's method, as sums of elaborate exponentials.
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The purpose cosh x has a Taylor series expression with only even exponents for x. Therefore it's a good operate, that is, symmetric with respect towards the y-axis. The sum from the sinh and cosh series will be the infinite series expression of the exponential function.
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coth x = cosh x sinh x = e x + e − x e x − e − x = displaystyle coth x= frac cosh x sinh x = frac e^ x +e^ -x e^ x -e^ useful source -x =
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