Abstract
A new set of polynomials is introduced. These polynomials arise from the Faulhaber–Jacobi formula for the sum of powers of integers, and are related to the Bernoulli numbers. Their asymptotic behaviour exhibits a discrete analogue of the Stokes phenomenon known from the asymptotics of differential equations. In this case, the usual exponential growth is replaced by algebraic growth and the Stokes lines are replaced by ‘Stokes points’. Error estimates are provided and the expansions are shown to be asymptotic.
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