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1. Recall the definition of hyperbolic functions.
cosh(t) = et + e-t/2 sinh (t) = et - 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-xxt-1 dx
If n is a positive integer then,
Γ(n+1) = n!
The Gamma function is an extension of the normal factorial function
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