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1·An asymptotic formula is given for the sum, where is the Eulers function.

设表示欧拉函数，用分析方法给出了的一个渐进公式。

2·This paper has investigated the system of congruences and given them the asymptotic formula of the number of solutions.

给出了一类同余方程组解数的公式或渐近公式。

3·Furthermore, the renewal equation and asymptotic formula of the distribution of the amount of the claim causing ruin are obtained.

此外，还得到了导致破产的索赔额的分布满足的瑕疵更新方程和渐近解。

4·The main purpose of this paper is to study the asymptotic properties of the third power mean and give a sharper asymptotic formula for it.

本文的主要目的是研究均值的渐近性质，并给出一个较强的渐近公式。

5·In this paper, we have studied the asymptotic formula of a number theoretic function about the primitive roots modulo n, and given a more precise asymptotic formula.

研究一个关于n原根的数论函数的渐近性质，给出了一个较为精确的渐近公式。

6·By using the limit theory, we discuss and prove the asymptotic properties of mean point in integral mean value formula for a complex function.

利用极限理论，给出了复函数积分中值公式的“中值点”的渐近性的简洁证明。

7·By using the limit theory, we discuss and prove the asymptotic properties of mean value point in differential mean value formula for a complex function.

利用极限理论，给出了复函数微分中值公式的“中值点”的渐近性的简洁证明。

8·The asymptotic behavior theorems of the midpoint of remainder in the midpoint formula and their applications are presented in this paper.

给出中点公式余项“中间点”的渐进性定理及其应用。

9·This paper firstly proves R-S mean value formula for integral, and USES the supplementary function for further discussing the asymptotic property of the intermediate point.

本文首先证明了R—S积分中值公式，并利用辅助函数进一步讨论了其“中间点”的渐近性。

10·By Newton algorithm and the analysis for asymptotic solution, this paper presents a direct formula for calculating critical depths of trapezoidal open channels.

依据牛顿算法及渐近解分析，本文提出了一种梯形明渠临界流方程的直接算法。