Research introduces new deranged Bell polynomials, revealing connections with other polynomial types.
In this paper, we introduce the deranged Bell polynomials as a natural generalization of the deranged Bell numbers defined by Belbachir et al. and investigate several of their interesting properties. Moreover, using umbral calculus, we express these polynomials as linear combinations of Bernoulli, Euler, Changhee, Daehee, and Bell polynomials, thereby revealing their interrelationships.
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Yun et al. (2026) studied this question.
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