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arXiv · 1401.2737

Higher Derivatives of the Falling Factorial and Related Generalizations of the Stirling and Harmonic Numbers

Steven S. Poon
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Abstract

Through a brute-force approach to calculating the higher derivatives of the falling factorial function, a number of interesting quantities were obtained and analyzed. In particular, it was found that a quantity that can be described as the "elementary symmetric harmonic sum" is a natural way to describe the solutions to such higher derivatives. The relationship of this type of generalized harmonic number to other quantities discussed in the literature, such as the r-Stirling numbers, was described in detail.

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Steven S. Poon. 2014-01-13. Higher Derivatives of the Falling Factorial and Related Generalizations of the Stirling and Harmonic Numbers. https://arxiv.org/abs/1401.2737

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