A New Generating Function of (q-) Bernstein-Type Polynomials and Their Interpolation Function
By Yilmaz Simsek, Mehmet Acikgoz. 2010
99 citations recorded by the source corpus.
The main object of this paper is to construct a new generating function of the () Bernstein-type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and derivative of the () Bernstein-type polynomials. We also give relations between the () Bernstein-type polynomials, Hermite polynomials, Bernoulli polynomials of higher order, and the second-kind Stirling numbers. By applying Mellin transformation to this generating function, we define interpolation of the () Bernstein-type polynomials. Moreover, we give some applications and questions on approximations of () Bernstein-type polynomials, moments of some distributions in Statistics.
Subfields: Computational Mechanics, Numerical Analysis, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/e688f1f6fd0a1c1d2157be1405a25e62e8a6a90f
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In Computational Mechanics
In Numerical Analysis
In Statistics and Probability
Citations in the corpus
- On the weighted q-Bernoulli numbers and polynomials (2010, methodology): “In this paper we use the following notation: [x]q = 1− q 1− q , (see [1-16]).”
- Functional equations from generating functions: a novel approach to deriving identities for the Bernstein basis functions (2011, methodology): “ns for the Bernstein basis functions. The Bernstein basis functions Bn k(x) are defined as follows: Definition 1. Bn k(x) = n k xk(1−x)n−k, (2.1) where n k = n! k!(n− k)! , k= 0,1,··· ,ncf. [1]-[13]. Generating functions for the Bernstein basis functions can be defined as follows: Definition 2. fB,k”
- A note on q-Bernstein polynomials (2010, methodology): “Recently, Simsek-Acikgoz([17]) and Kim-Jang-Yi([9]) have studied the q-extension of Bernstein polynomials, which are different Phillips q-Bernstein polynomials.”