Open AccessOnp‐Adic Analogue ofq‐Bernstein Polynomials and Related Integrals
Author(s) -
T. Kim,
J. Choi,
Y. H. Kim,
Lee-Chae Jang
Publication year - 2010
Publication title -
discrete dynamics in nature and society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.264
H-Index - 39
eISSN - 1607-887X
pISSN - 1026-0226
DOI - 10.1155/2010/179430
Subject(s) - bernstein polynomial , mathematics , difference polynomials , orthogonal polynomials , wilson polynomials , macdonald polynomials , classical orthogonal polynomials , hahn polynomials , discrete orthogonal polynomials , pure mathematics , type (biology) , gegenbauer polynomials , algebra over a field , ecology , biology
Recently, Kim's work (in press) introduced -Bernstein polynomials which are different Phillips' -Bernstein polynomials introduced in the work by (Phillips, 1996; 1997). The purpose of this paper is to study some properties of several type Kim's -Bernstein polynomials to express the -adic -integral of these polynomials on ℤ associated with Carlitz's -Bernoulli numbers and polynomials. Finally, we also derive some relations on the -adic -integral of the products of several type Kim's -Bernstein polynomials and the powers of them on ℤ
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