A note on characteristic function for Bernstein polynomials involving special numbers and polynomials
Buket Şimşek
Abstract
The aim of this present paper is to establish and study generating function associated with a characteristic function for the Bernstein polynomials. By this function, we derive many identities, relations and formulas relevant to moments of discrete random variable for the Bernstein polynomials (binomial distribution), Bernoulli numbers of negative order, Euler numbers of negative order and the Stirling numbers.
Topics & Concepts
MathematicsDifference polynomialsBernstein polynomialDiscrete orthogonal polynomialsClassical orthogonal polynomialsWilson polynomialsHahn polynomialsGenerating functionStirling numberBernoulli polynomialsStirling numbers of the second kindOrthogonal polynomialsMacdonald polynomialsGegenbauer polynomialsPure mathematicsBernoulli numberOrder (exchange)Bell polynomialsRecurrence relationDiscrete mathematicsCombinatoricsFinanceEconomicsAdvanced Mathematical IdentitiesAdvanced Combinatorial MathematicsAdvanced Mathematical Theories and Applications