Comptes Rendus
no. 9-10
Théorie des fonctions, Combinatoire
New asymptotic expansions on hyperfactorial functions
Jianjun Xu1
1 Institute of Mathematics, Jilin University, Changchun 130012, China
Comptes Rendus. Mathématique, Volume 358 (2020) no. 9-10, pp. 971-980.

In this paper, by using the Bernoulli numbers and the exponential complete Bell polynomials, we establish four general asymptotic expansions for the hyperfactorial functions ∏ k=1 n k k q , which have only odd power terms or even power terms. We derive the recurrences for the parameter sequences in these four general expansions and give some special asymptotic expansions by these recurrences.

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DOI : 10.5802/crmath.73
Classification : 41A60, 05A15
Jianjun Xu 1

1 Institute of Mathematics, Jilin University, Changchun 130012, China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {New asymptotic expansions on hyperfactorial functions},
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Jianjun Xu. New asymptotic expansions on hyperfactorial functions. Comptes Rendus. Mathématique, Volume 358 (2020) no. 9-10, pp. 971-980. doi : 10.5802/crmath.73. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.73/

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