Geodesic
On Binomial coefficients of real arguments
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 514-523.

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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.
Keywords: factorial, gamma function
Mots-clés : binomial coefficient, real binomial coefficient. 
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T. I. Fedoryaeva. On Binomial coefficients of real arguments. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 514-523. http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a22/

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