查询词典 maclaurin formula

This essay deduces the power sum formula of an arbitrary arithmetic progression step by step on the basis of Euler-Maclaurin formula,and then achieres the compute formula of natural number power sum -∑ni=1i m.

前n个自然数的方幂和，∑ni=1im是一个古老的难题。

By introducing two pairs of conjugate exponent parameters and, and using the improved Euler-Maclaurin＇s summation formula for estimating the weight coefficient, a reverse Hilbert-type inequality with a best constant factor is proved.

本文通过引入两对共轭指数参量与及应用改进的Euler-Maclaurin求和公式以估算权系数，证明了一个具有最佳常数因子的逆向Hilbert型不等式；作为应用，还给出了相应的等价式及一些特殊结果。

Through the polynomial approximation to function, resulting in more than a Peano-type and Lagrange remainder of the Taylor formula, using elementary functions Maclaurin expansions to address the limits and the approximate evaluation of the problem.

通过多项式来逼近函数，从而得到带有佩亚诺型余项和拉格朗日余项的泰勒公式，利用初等函数的麦克劳林展开式来解决极限及近似求值的问题。

When, the Taylor's formula with Lagrange Remainder term of order simplifies the Maclaurin's Formula with Lagrange Remainder term of order, which is in form of following

当时，带有拉格朗日型余项的阶泰勒公式简化为带有拉格朗日余项型的阶麦克劳林公式，形式如下

Firstly, the Signal Noise Ratio characteristic of matched filter despread symbol and the distribution of coherent phase estimation error are derived. Secondly, the exact integration formula of BER for fading channel is presented, moreover, by using the Maclaurin series expansion of MPSK conditional Symbol Error Rate, the simplified BER approximations for BPSK and QPSK are derived over AWGN, Nakagami-m fading and Rayleigh fading channel.

首先推导了匹配滤波解扩符号的信噪比特性和相干相位估计误差的分布；然后给出了衰落信道中误比特率的精确积分式，并利用MPSK条件误符号率的麦克劳林级数形式，推导了AWGN，Nakagami-m衰落和瑞利衰落信道中BPSK，QPSK误比特率的简化逼近式。

Based on the analysis of some aspects, such as the approximative algorithm of FOC, the Tustin transform theory and its generating function formula's character, the convergence guarantee of binomial power function by Maclaurin expanding, and the consideration of the limitation of conventional methods, an improved method is proposed to compute the numerical evalution of FOC using PSE and Tustin transform and is further applied to solving the linear FOS.

以分数阶算子近似方法的分析研究为基础，基于Tustin变换理论及其用于分数阶算子的离散生成函数公式特点，利用二项式幂函数的Maclaurin展开能够保证收敛的特性，考虑常用算法的局限性，提出了一种改进的基于幂级数展开和Tustin变换的分数阶运算方法，并应用于线性分数阶系统的求解，给出了递推算法的详细推导。

Starting from the steady-state performance of three-phase fully-controlled rectified circuit, which is with large inductive load, we take the front two items of the Maclaurin series of the DC voltage average as approximate formula, with considering of the effect of the AC-side inductance first, and further effect of AC resistance on DC voltage and commutation angle.

本文从带有高感性直流负载的三相全控整流电路稳态工作的物理情况出发，首先考虑了交流侧电感的影响，进而考虑交流侧电阻对直流电压、换相角的影响，将直流电压的平均值用麦克劳林级数表示，取前两项作近似，得出了实用的解析计算公式，并给出了计算步骤，实验证明该结果具有较高的精度。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失