New asymptotic expansions on hyperfactorial functions
In this paper, by using the Bernoulli numbers and the exponential complete Bell polynomials, we establish four general asymptotic expansions for the hyperfactorial functions $\prod _{k=1}^n {k^{k^q}}$, which have only odd power terms or even power terms. We derive the recurrences for the parameter s...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2021-01-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.73/ |
| _version_ | 1797651542518530048 |
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| author | Xu, Jianjun |
| author_facet | Xu, Jianjun |
| author_sort | Xu, Jianjun |
| collection | DOAJ |
| description | In this paper, by using the Bernoulli numbers and the exponential complete Bell polynomials, we establish four general asymptotic expansions for the hyperfactorial functions $\prod _{k=1}^n {k^{k^q}}$, 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. |
| first_indexed | 2024-03-11T16:17:18Z |
| format | Article |
| id | doaj.art-706a469091694edc9f3c7037f9a98c30 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:17:18Z |
| publishDate | 2021-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-706a469091694edc9f3c7037f9a98c302023-10-24T14:18:48ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692021-01-013589-1097198010.5802/crmath.7310.5802/crmath.73New asymptotic expansions on hyperfactorial functionsXu, Jianjun0Institute of Mathematics, Jilin University, Changchun 130012, ChinaIn this paper, by using the Bernoulli numbers and the exponential complete Bell polynomials, we establish four general asymptotic expansions for the hyperfactorial functions $\prod _{k=1}^n {k^{k^q}}$, 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.73/ |
| spellingShingle | Xu, Jianjun New asymptotic expansions on hyperfactorial functions Comptes Rendus. Mathématique |
| title | New asymptotic expansions on hyperfactorial functions |
| title_full | New asymptotic expansions on hyperfactorial functions |
| title_fullStr | New asymptotic expansions on hyperfactorial functions |
| title_full_unstemmed | New asymptotic expansions on hyperfactorial functions |
| title_short | New asymptotic expansions on hyperfactorial functions |
| title_sort | new asymptotic expansions on hyperfactorial functions |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.73/ |
| work_keys_str_mv | AT xujianjun newasymptoticexpansionsonhyperfactorialfunctions |