5,354 research outputs found
On The Properties Of -Bernstein-Type Polynomials
The aim of this paper is to give a new approach to modified -Bernstein
polynomials for functions of several variables. By using these polynomials, the
recurrence formulas and some new interesting identities related to the second
Stirling numbers and generalized Bernoulli polynomials are derived. Moreover,
the generating function, interpolation function of these polynomials of several
variables and also the derivatives of these polynomials and their generating
function are given. Finally, we get new interesting identities of modified
-Bernoulli numbers and -Euler numbers applying -adic -integral
representation on and -adic fermionic -invariant integral
on , respectively, to the inverse of -Bernstein polynomials.Comment: 17 pages, some theorems added to new versio
On a class of -Bernoulli, -Euler and -Genocchi polynomials
The main purpose of this paper is to introduce and investigate a class of
-Bernoulli, -Euler and -Genocchi polynomials. The -analogues of
well-known formulas are derived. The -analogue of the Srivastava--Pint\'er
addition theorem is obtained. Some new identities involving -polynomials are
proved
Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis
In the present paper, we obtain new interesting relations and identities of
the Apostol-Bernoulli polynomials of higher order, which are derived using a
Bernoulli polynomial basis. Finally, by utilizing our method, we also derive
formulas for the convolutions of Bernoulli and Euler polynomials, expressed via
Apostol-Bernoulli polynomials of higher order.Comment: 8 pages, submitte
General Convolution Identities for Bernoulli and Euler Polynomials
Using general identities for difference operators, as well as a technique of
symbolic computation and tools from probability theory, we derive very general
kth order (k \ge 2) convolution identities for Bernoulli and Euler polynomials.
This is achieved by use of an elementary result on uniformly distributed random
variables. These identities depend on k positive real parameters, and as
special cases we obtain numerous known and new identities for these
polynomials. In particular we show that the well-known identities of Miki and
Matiyasevich for Bernoulli numbers are special cases of the same general
formula.Comment: 20 page
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