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The typical fourier series is...

y = SUM{aSin(nx)} + SUM{bCos(nx)}

I think I will attempt

y = SUM{aSin(nx^2)} + SUM{bCos(nx^2)}

replacing x -->x^2 should give me the "smushing" that I want.

The application is bladder level as a function of beers consumed. The basic function is an increasing (quadratic, exponential) function followed by a linear, steeply sloped drop to zero.