In GI Taylor's historic paper on swimming microorganisms, a two-dimensional sheet was
proposed as a model for flagellated cells passing traveling waves as a means of locomotion.
Using a perturbation series, Taylor computed swimming speeds up to fourth order in
amplitude. Here we systematize the expansion so that it can be carried out formally to
arbitrarily high order. The resultant series diverges for an order one value of the wave
amplitude, but may be transformed into a series with much improved convergence …