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For example, the circle method of Hardy and Littlewood was conceived as applying to power series near the unit circle in the complex plane; it is now thought of in terms of finite exponential sums (that is, on the unit circle, but with the power series truncated).
The classical virial expansion expresses the pressure of a many-particle system in equilibrium as a power series in the density.
Finally, in the 1970s E.G.D. Cohen and J.R. Dorfman proved that a systematic (power series) extension of the Boltzmann equation to high densities is mathematically impossible.
In that time the alternatives for professional digital image editing were over-200k-and-more-USD dedicated workstations like Quantel's Paintbox, Crossfield or Barco Creator software running on expensive SGI Power series multiprocessor boxes.