Bounds for the zeros of symmetric kravchuk polynomials - Area, Ivan; Dimitrov, Dimitar K. [UNESP]; Godoy, Eduardo; Paschoa, Vanessa (Springer, 2015)
Sharp bounds for the zeros of symmetric Kravchuk polynomials K (n) (x;M) are obtained. The results provide a precise quantitative meaning of the fact that Kravchuk polynomials converge uniformly to Hermite polynomials, as M tends to infinity. They show also how close the corresponding zeros of two polynomials from these sequences of classical orthogonal polynomials are.
Keywords: Orthogonal polynomials of a discrete variable; Symmetric Kravchuk polynomials; Hermite polynomials; Limit relation; Zeros