Say a function is *ethereal* iff:

1. all the coefficients in the power series representation of it are transcendental

2. there is no easy way of getting at those coefficients

2 is a crapshoot. Let me give a somewhat contrived example, take the Airy function , which has power series representation:

. I don’t consider this function ethereal because the coefficients are easy to get at, so to speak.

Now consider a function whose power series coefficients are such that . There is a sea of such functions, but they’re sort of slippery and hard to make

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