ON BINOMIAL COEFFICIENTS OF REAL ARGUMENTS

As is well-known, a generalization of the classical concept of the factorial n! for a real number x is an element of 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 (r alpha) of real arguments r, alpha is an element of 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.