John D. Cook • 7/26/2026

exp_q

This article defines the function expq(x), which is derived from the exponential power series by retaining only terms whose index is a multiple of q. It provides closed-form expressions using complex roots of unity, discusses its appearance in differential equations (e.g., functions equal to their third or fourth derivative), and shows how to implement it in Mathematica via the Mittag-Leffler function. The article also hints at combinatorial applications. It is a technical math article relevant to computer science and mathematical computing.

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#Differential Equations #Power Series #Discrete Fourier Transform