三角级数求和的两种方法

借助实例介绍如何利用傅立叶级数和复变函数的幂级数这两种工具解决有关三角级数的求和问题.     

概率方法在级数求和中的应用

本文的目的是通过一些例子说明如何应用概率方法求某些无穷级数的和。     

含参变量富里叶级数的Laplace变换求和法

本文建立了含参变量富里叶级数的Laplace变换求和定理.利用Laplace变换表可以求得许多在力学上有重要应用的新的含参变量富里叶级数的和式.     

级数求和方法

级数求和是级数理论的基本问题之一,也是较难解决的问题.本文将从几个不同的角度对级数求和的方法作一探讨.     

一类级数的求和

给出了一类级数的求和公式,并列举其应用.     

级数求和的解题策略

级数求和可选择采用化繁为简、局部与整体、分合并用、映射化归、虚实互化、正难则反等解题策略.     

与中心数相关的一类级数求和公式

This paper provides a pair of summation formulas for a kind of combinatorial series involvingak＋b m as a factor of the summand. The construction of formulas is based on a certain series transformation formula [2, 7, 9] and by making use of the C-numbers [3]. Various consequences and examples including several remarkable classic identities are presented to illustrate some applications of the formulas obtained.     

两个级数求和问题的概率模型

通过构造概率模型,应用概率论与数理统计的方法给出两个特殊级数的求和问题.     

两个级数的求和问题

本文讨论级数(1)和级数(2)的求和问题,得出其求和公式(3)、(4).     

三角级数在Burgers-KdV混合型方程中的应用

利用三角级数法将Burgers-KdV混合型方程转化为一组非线性代数方程,进而用待定系数法求解方程组,最后求出了Burgers-KdV混合型方程的精确解.     

Euler-Maclaurin Summation of Trigonometric Fourier Series

Trigonometric Fourier series are, in general, difficult to sum to high accuracy. An example is given by the series in which α and β(>0) are rational numbers satisfying 0<β/α≤1, where λ is an independent variable and j is a positive integer or zero. This paper presents a method for the efficient evaluation of the sum of such series. Fourier series which are the real or the imaginary part of , but which are not explicitly expressible as simple polynomials in λ, are obtained as the sum of a logarithic term and an infinite series in powers of λ, whose expansion is valid when 0<λ≤(2π/α) and is exact. When the Fourier series is expressible as a polynomial in λ, the method identifies that polynomial.     

On Summation of Nonharmonic Fourier Series

Let a sequence \(\Lambda \subset {\mathbb {C}}\) be such that the corresponding system of exponential functions \({\mathcal {E}}(\Lambda ):=\left\{ {\text {e}}^{i\lambda t}\right\} _{\lambda \in \Lambda }\) is complete and minimal in \(L^2(-\pi ,\pi )\), and thus each function \(f\in L^2(-\pi ,\pi )\) corresponds to a nonharmonic Fourier series in \({\mathcal {E}}(\Lambda )\). We prove that if the generating function \(G\) of \(\Lambda \) satisfies the Muckenhoupt \((A_2)\) condition on \({\mathbb {R}}\), then this series admits a linear summation method. Recent results show that the \((A_2)\) condition cannot be omitted.     

On Fourier Series on the Torus and Fourier Transforms

Mathematical Notes - The question of the representability of a continuous function on $$mathbb R^d$$ in the form of the Fourier integral of a finite Borel complex-valued measure on $$mathbb R^d$$...     

Summation of Fourier Series on the Infinite-Dimensional Torus

Conditions for the convergence of Fejér means for functions on the infinite-dimensional torus over cubes and rectangles are obtained, and a generalization of these results to the case of products of abstract measure spaces is proposed.

     

Rectangular Summation of Multiple Fourier Series and Multi-parametric Capacity

Potential Analysis - We consider the class of multiple Fourier series associated with functions in the Dirichlet space of the polydisc. We prove that every such series is summable with respect to...     

A New Method of Summation of Fourier Series Converging in C-Norm

A new method is based on some properties of a semigroup of fractional powers of some positive operator in Banach space. This method uses an essentially smaller deformation of an ordinary partial sum of the Fourier series than in Cesaro's method or in its generalizations.     

On the Generalized Cesáro Summability of Trigonometric Fourier Series

The class of generalized bounded variation is considered. For functions from this class, the deviation of the generalized Cesáro means of negative order in the norm of L^r, (1 ≤ r ≤ ∞) is estimated.

     

On Exponential Summability of Rectangular Partial Sums of Double Trigonometric Fourier Series

In this paper, we study the a.e. exponential strong summability problem for the rectangular partial sums of double trigonometric Fourier series of functions in L logL.     

Almost Everywhere Convergence of Multiple Trigonometric Fourier Series of Functions from Sobolev Classes

Mathematical Notes - In this paper, we study the almost everywhere convergence of spherical partial sums of multiple Fourier series of functions from Sobolev classes. It is proved that almost...