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arXiv · 2012.00882

The Generalized Superfactorial, Hyperfactorial and Primorial functions

Vignesh Raman
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Abstract

This paper introduces a new generalized superfactorial function (referable to as $n^{th}$- degree superfactorial: $sf^{(n)}(x)$) and a generalized hyperfactorial function (referable to as $n^{th}$- degree hyperfactorial: $H^{(n)}(x)$), and we show that these functions possess explicit formulae involving figurate numbers. Besides discussing additional number patterns, we also introduce a generalized primorial function and 2 related theorems. Note that the superfactorial definition offered by Sloane and Plouffe (1995) is the definition considered (and not Clifford Pickover's (1995) superfactorial function: $n\$$).

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Vignesh Raman. 2020-12-01. The Generalized Superfactorial, Hyperfactorial and Primorial functions. https://arxiv.org/abs/2012.00882

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