using sinh(x) ?

[tommy1729]

im thinking about using asymt of exp(x) to solve tetration.

perhaps not the best one , but sinh(x) comes to my mind.

if we take the half-iterate of sinh(x) by using taylor series , we get a good approximation of the half-iterate of exp(x) for x large.

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is there a problem with the half-iterate of sinh(x) ? does its taylor series radius = 0 ?
is the inner radius of the mittag-leffler = 0 ?

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