Definition of hyperbolic functions

Question

1. Recall the definition of hyperbolic functions.

cosh(t) = e^t + e^-t/2 sinh (t) = e^t - e^-t/2

2. Be careful when using "normal" trig function vs. hyperbolic functions. The only difference in the formulas is the " +a² 2 " for the "normal" trig functions becomes a "- a² " for the hyperbolic functions!

3. Formula uses the Gamma function which is defined as

Γ(t) = _o∫^∞ e^-xx^t-1 dx

If n is a positive integer then,

Γ(n+1) = n!

The Gamma function is an extension of the normal factorial function