Closed-Form Formulas for the nth Derivative of the Power-Exponential Function xx
Symmetry(2023)
Abstract
In this paper, the authors give a simple review of closed-form, explicit, and recursive formulas and related results for the nth derivative of the power-exponential function xx, establish two closed-form and explicit formulas for partial Bell polynomials at some specific arguments, and present several new closed-form and explicit formulas for the nth derivative of the power-exponential function xx and for related functions and integer sequences.
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Key words
power-exponential function,derivative,closed-form formula,explicit formula,recursive formula,Comtet's number,integer sequence,partial Bell polynomial
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