Abstract
These numbers are defined as the coefficients of the Euler–Frobenius polynomialswhich usually are introduced via the rational function expansionn being a nonnegative integer and λ∈[0, 1). The special case An, l (0) is known from combinatorics (Eulerian numbers) and the general one An, l (λ) occurs, for example, in approximation theory, summability, and rounding error analysis. By supplementing and extending known results on Eulerian numbers, various theorems for the Euler–Frobenius numbers An, l(λ) and related quantities are established including unimodality, monotonicity properties, and asymptotic expansions given by a local central limit theorem.
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