power sum

Relationship between Bernoulli polynomial and power sum polynomial;

Bernoulli多项式与幂和多项式的关系

With the method of coefficients comparison,this paper makes improvement to a classic formula on power sum of successive natural numbers,educes three groups of calculating formulas on the coefficients of the power sum,and puts forward four conjectures.

利用比较系数法,改进了传统的连续自然数等幂和的计算公式,得到了3组具体的计算公式,提出了4个猜想。

This essay deduce s the power sum formula of an arbitrary arithmetic progression step by step on t he basis of Euler-Maclaurin formula,and then achieres the compute formula of nat ural number power sum-∑mi=1im.

前n个自然数的方幂和 ,∑mi=1im(简称等幂和 )是一个古老的难题 ,从著名的Euler-Maclaurin定理出发 ,给出了任意一个等差列方幂和公式 ,更一般地得到了等幂和的计算公式 。

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(简称等幂和 )是一个古老的难题 。

In this paper, by using the binomial theorem, we obtain a new recursion formula for power sum problem ∑ ni=1i k .

利用二项式定理得到了关于整数幂和∑ni=1ik的一个新的递推公式,并由此得出幂和问题的一个性质和k=8,9,10,11时幂和的计算公式。

Consequently we obtain some new proposition for the power sum problem.

并由此得出幂和问题的一些新的性质。

And thus we ve worked out a new recursion formula of power sum problem ,using it ,we can get the calculationg formula of all the power sum problem.

本文利用二项式定理得到K =8,9,10 ,11时幂和∑ni=1ik 的计算公式 ,较文[1 ] 中结果表达式简单 ,并推出了关于幂和问题的一个新的递推公式 ,利用它可导出所有幂和问题的计算公式 。

The a simple and convenient method for sum of equal powers and Bernoulli s number;

等幂和与Bernoulli数的简捷方法

Let p be odd prime number, an be last digits of sum of equal powers at 2p system.

设p为奇素数,αn为等幂和表成2p进制的末位数字,获得等幂和的同余性与等幂和的周期性,从而证明当p-1×m时,αn是最小正周期为4p的周期数列;当p-1│m时,αn是最小正周期为4p2的周期数列,并且完全确定当等幂和表成10进制时的末位数字αn,等幂和的数论性质对G。

A succinct expression and cycl integrating no the sum of equal powers are obtained here and the value of the formula B 1～B 1000  is given.

Bernoulli数与等幂和Sm(n) =1 m+2 m+… +nm 是一个古老的难题 ,在数论研究中有着重要的作用 。

Recurrence formula for the coefficients of the sum of equal power series;

等幂和系数的一个递推公式

This paper improves the unique of the general formula of the sum of equal power series by difference.

利用差分论证了等幂和一般公式的唯一性,它可用插值法构造,也可用待定系数法求得。

In this paper, a general formula of sum of equal power series of natural number is given.

本文利用函数项级数，微分及排列组合等工具推导出了一个求自然数等幂和的一个一般公式。

Generating Funtion and a New Calculating Formula of the Sum Power of Natural Numbers

幂和序列的生成函数与幂和新的计算公式

On the General Form of Lucas Number Power Sum;

关于Lucas数方幂和的一般形式

ON sum of like powers k∑i=1 i~n;

关于等幂和sum from i=1 to k(i~n)

The Exponent of Factor 5 in Power Sum Alternated with Positive and Negative;

一类正负相间方幂和中因子5的指数

On the Congruences Relation of Sum od Equal Powers and Stirling Numbers;

等幂和与Stirling数的同余关系

The a simple and convenient method for sum of equal powers and Bernoulli s number;

等幂和与Bernoulli数的简捷方法

On the Sum of Equal Powers and Diophantine Equation S_5(x) =y~n;

关于幂和丢番图方程S_5(x)=y~n

Purely Idempotent Latin Squares and Purely Symmetric Idempotent Latin Squares;

纯的幂等拉丁方和纯的对称幂等拉丁方

On Characteristics of(m,l)Rank-idempotent Matrix and(m,l)Idempotent Matrix

(m,/)秩幂等矩阵和(m,/)幂等矩阵的特性研究

The general solution of (5.122) is an arbitrary linear combination of a series of even powers and a series of odd powers.

（5．122）的通解是一个偶次幂级数和一个奇次幂级数的任意线性组合。

Study on the rheology of dry foam fracturing fluid using power-law (PL) model and modified power-law (PL) model

应用幂律和改良幂律模型研究干法泡沫压裂液流变性

Primitiveness of Character Triples and X-Nilpotent Group;

特征标三元组的本原性和X-幂零群

The p～＊-Nilpotency and θ-Pairs for Subgroups on Finite Groups;

有限群的p～＊-幂零性和子群的θ-子群偶

The Application of Difference in Summing the Powes of K Degrees of the Positive Integers;

差分的应用及正整数的k次方幂求和

On the Prime Powers in Sums of Squares of Consecutive Positive Integers;

关于连续正整数平方和中的素数方幂

The prime powers in sums of squares of 4k consecutive positive integers;

4k个连续正整数平方和中的素数方幂

Deduction of Sum Formula of Natural Number High Power;

自然数高次幂的求和公式的一种推导

Mathematical Recreation(Ⅴ):Generalized Fibonacci's Number and Sum of Power Series

数学娱乐(五)——推广Fibonacci数列与幂级数和