On binomial coefficients of real arguments Full article
| Journal |
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2023, Volume: 20, Number: 1, Pages: 514-523 Pages count : 10 DOI: 10.33048/semi.2023.20.031 | ||
| Tags | factorial, binomial coefficient, gamma function, real binomial coefficient. | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0018 |
Abstract:
As is well-known, a generalization of the classical concept of the factorial n! for a real number $x\in {\mathbb R}$ is the value of Euler's gamma function $\Gamma(1+x)$. In this connection, the notion of a binomial coefficient naturally arose for admissible values of the real arguments. We prove by elementary means a number of properties of binomial coefficients $\binom{r}{\alpha}$ of real arguments $r,\,\alpha\in {\mathbb R}$\, such as analogs of unimodality, symmetry, Pascal's triangle, etc. for classical binomial coefficients. The asymptotic behavior of such generalized binomial coefficients of a special form is established.
Cite:
Fedoryaeva T.I.
On binomial coefficients of real arguments
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. V.20. N1. P.514-523. DOI: 10.33048/semi.2023.20.031 WOS Scopus РИНЦ
On binomial coefficients of real arguments
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. V.20. N1. P.514-523. DOI: 10.33048/semi.2023.20.031 WOS Scopus РИНЦ
Dates:
| Submitted: | May 11, 2022 |
| Accepted: | Jun 6, 2023 |
| Published print: | Jul 18, 2023 |
| Published online: | Jul 18, 2023 |
Identifiers:
| Web of science: | WOS:001034303400002 |
| Scopus: | 2-s2.0-85167904825 |
| Elibrary: | 54768303 |
Citing:
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