共查询到20条相似文献,搜索用时 15 毫秒
1.
Djurdje Cvijovi? 《Journal of Mathematical Analysis and Applications》2008,337(1):169-173
Haruki and Rassias [H. Haruki, T.M. Rassias, New integral representations for Bernoulli and Euler polynomials, J. Math. Anal. Appl. 175 (1993) 81-90] found the integral representations of the classical Bernoulli and Euler polynomials and proved them by making use of the properties of certain functional equation. In this sequel, we rederive, in a completely different way, the results of Haruki and Rassias and deduce related and new integral representations. Our proofs are quite simple and remarkably elementary. 相似文献
2.
Shy-Der Lin 《Journal of Mathematical Analysis and Applications》2004,294(2):399-411
The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated single-, double-, and triple-integral representations. Some known or new consequences of the general results presented here, involving such classical orthogonal polynomials as the Jacobi, Laguerre, Hermite, and Bessel polynomials, and various other relatively less familiar hypergeometric polynomials, are also considered. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials. 相似文献
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4.
In this paper, a finite Chebyshev expansion is developed to solve Volterra integral equations with logarithmic singularities
in their kernels. The error analysis is derived. Numerical results are given showing a marked improvement in comparison with
the piecewise polynomial collocation method given in literature. 相似文献
5.
Lorenzo DAmbrosio 《Journal of Approximation Theory》2006,140(2):191-202
The purpose of this paper is to study some new concrete approximation processes for continuous vector-valued mappings defined on the infinite dimensional cube or on a subset of a real Hilbert space. In both cases these operators are modelled on classical Bernstein polynomials and represent a possible extension to an infinite dimensional setting.The same idea is generalized to obtain from a given approximation process for function defined on a real interval a new approximation process for vector-valued mappings defined on subsets of a real Hilbert space. 相似文献
6.
《Indagationes Mathematicae》2022,33(4):801-815
We consider the irreducibility of polynomial where is a negative integer. We observe that the constant term of vanishes if and only if . Therefore we assume that where is a non-negative integer. Let and more general polynomial, let where with are integers such that . Schur was the first to prove the irreducibility of for . It has been proved that is irreducible for . In this paper, by a different method, we prove: Apart from finitely many explicitly given possibilities, either is irreducible or is linear factor times irreducible polynomial. This is a consequence of the estimate whenever has a factor of degree and . This sharpens earlier estimates of Shorey and Tijdeman and Nair and Shorey. 相似文献
7.
研究了代数多项式导数的Bernstein不等式和Markov不等式.通过代数多项式导数的一个积分表示式,给出这两个著名不等式以及它们的离散形式的证明. 相似文献
8.
Daniel Carando Ignacio Zalduendo 《Proceedings of the American Mathematical Society》1999,127(1):241-250
We study the problem of extendibility of polynomials over Banach spaces: when can a polynomial defined over a Banach space be extended to a polynomial over any larger Banach space? To this end, we identify all spaces of polynomials as the topological duals of a space spanned by evaluations, with Hausdorff locally convex topologies. We prove that all integral polynomials over a Banach space are extendible. Finally, we study the Aron-Berner extension of integral polynomials, and give an equivalence for non-containment of .
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In this paper we prove someL
P inequalities for polynomials, wherep is any positive number. They are related to earlier inequalities due to A Zygmund, N G De Bruijn, V V Arestov, etc. A generalization
of a polynomial inequality concerning self-inversive polynomials, is also obtained. 相似文献
11.
P. Malits 《Journal of Mathematical Analysis and Applications》2003,281(1):205-220
New integral representations, asymptotic formulas, and series expansions in powers of tanh(t/2) are obtained for the imaginary and real parts of the Legendre function Piξ(cosht). Coefficients of these series expansions are orthogonal polynomials in the real variable ξ. A number of relations for these orthogonal polynomials are obtained on the basis of the generating function. Several inversion theorems are proven for the integral transforms involving the Legendre function of imaginary degree. In many cases it is preferable to employ these transforms, than Mehler-Fok transforms, since conditions placed on functions are less restrictive. 相似文献
12.
Abdullah Alt?n 《Journal of Mathematical Analysis and Applications》2009,353(1):121-1933
The main object of this paper is to construct a systematic investigation of a multivariable extension of the extended Jacobi polynomials and give some relations for these polynomials. We derive various families of multilinear and multilateral generating functions. We also obtain relations between the polynomials extended Jacobi polynomials and some other well-known polynomials. Other miscellaneous properties of these general families of multivariable polynomials are also discussed. Furthermore, some special cases of the results are presented in this study. 相似文献
13.
Daniel Carando Veró nica Dimant 《Proceedings of the American Mathematical Society》2007,135(6):1769-1773
We show that for every infinite-dimensional normed space and every there are extendible -homogeneous polynomials which are not integral. As a consequence, we prove a symmetric version of a result of John.
14.
We introduce a new family of multiple orthogonal polynomials satisfying orthogonality conditions with respect to two weights on the positive real line, with the gamma density and a density related to the exponential integral . We give explicit formulas for the type I functions and type II polynomials, their Mellin transform, Rodrigues formulas, hypergeometric series, and recurrence relations. We determine the asymptotic distribution of the (scaled) zeros of the type II multiple orthogonal polynomials and make a connection to random matrix theory. Finally, we also consider two related families of mixed-type multiple orthogonal polynomials. 相似文献
15.
Tamá s Erdé lyi Harvey Friedman 《Transactions of the American Mathematical Society》2005,357(3):999-1011
Given 2$">, we establish a good upper bound for the number of multivariate polynomials (with as many variables and with as large degree as we wish) with integer coefficients mapping the ``cube' with real coordinates from into . This directly translates to a nice statement in logic (more specifically recursion theory) with a corresponding phase transition case of 2 being open. We think this situation will be of real interest to logicians. Other related questions are also considered. In most of these problems our main idea is to write the multivariate polynomials as a linear combination of products of scaled Chebyshev polynomials of one variable.
16.
Rodica D. Costin 《Journal of Approximation Theory》2009,161(2):787-801
A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a three term recurrence relation, integral inter-relations, and weak orthogonality relations. 相似文献
17.
This paper is concerned with obtaining approximate numerical solutions of some classes of integral equations by using Bernstein polynomials as basis. The integral equations considered are Fredholm integral equations of second kind, a simple hypersingular integral equation and a hypersingular integral equation of second kind. The method is explained with illustrative examples. Also, the convergence of the method is established rigorously for each class of integral equations considered here. 相似文献
18.
A. Aziz W. M. Shah 《分析论及其应用》2007,23(2):101-111
In this paper we establish Lq inequalities for polynomials, which in particular yields interesting generalizations of some Zygmund-type inequalities. 相似文献
19.
主要研究勒让德多项式与契贝谢夫多项式之间的关系的性质,利用生成函数和函数级数展开的方法,得出了勒让德多项式与契贝谢夫多项式之间的一个重要关系,这对勒让德多项式与契贝谢夫多项式的研究有一定的推动作用. 相似文献
20.
In this paper, we propose a multi-projection and iterated multi-projection methods for Fredholm integral equations of the second kind with a smooth kernel using polynomial bases. We obtain super-convergence rates for the approximate solutions, more precisely, we prove that in M-Galerkin and M-collocation methods not only iterative solution approximates the exact solution u in the supremum norm with the order of convergence n-4k, but also the derivatives of approximate the corresponding derivatives of u in the supremum norm with the same order of convergence, n being the degree of polynomial approximation and k being the smoothness of the kernel. 相似文献