On Binomial coefficients of real arguments
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As is well-known, a generalization of the classical concept of the factorial n! for a real number x∈ℝ is the value of Euler's gamma function Γ(1+x). In this connection, the notion of a binomial coefficient naturally arose for admissible values of the real arguments. By elementary means, it is proved a number of properties of binomial coefficients rα of real arguments r, α∈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.
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