exp^[3/2](x) > sinh^[1/2](exp(x)) ?

[tommy1729]

Although it might appear like a random question to some , this is a rather important question :

Prove or disprove :

For any real x and exp^[3/2] computed with the 2sinh method :

exp^[3/2](x) > sinh^[1/2](exp(x))

***

I assume that both the first and second derivative of sinh^[1/2](x) for x >0 are positive.

The answer to these will lead to more progress !

And possibly some counterintuitive things !

regards

tommy1729