>       (d) I suspect that this handwave (and it is a big one) can be made
> rigorous by means of the calculus of variations,  turning the local
> maximization of entropy subject to int[f(x)dx]=1 into a differential
> equation to which these are the solutions. (But I've never tried.)

This is done by Chris Bishop in his book, Neural Networks for Pattern
Recognition, section 6.10.
.
.
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