关于Dedekind和的均值公式

本文的主要目的是利用ＤｉｒｉｃｈｌｅｔＬ－函数的均值定理研究Ｄｅｄｅｋｉｎｄ和的值分布性质，并给出一个较强的均值公式．     

双变量部分theta函数的乘积公式与性质

本文研究一类新的双变量部分theta函数,它是经典部分theta函数的推广,主要围绕这类函数的乘积公式、递推关系、级数展开等性质展开讨论.作为主要结果,我们建立了任意两个双变量部分theta函数的乘积公式,推广了Andrews-Warnaar经典部分theta函数的乘积公式,发现了双变量部分theta函数所满足的二阶递...     

关于广义Dedekind和的2k次均值

本文利用 Ｄｉｒｉｃｈｌｅｔ Ｌ－函数的均值定理,研究广义 Ｄｅｄｅｋｉｎｄ和的渐近性质,并给出一个有趣的渐近公式．     

一类不定积分的巧解

讨论一类分母为多项式二次幂的有理分式的特殊积分法,得到积分公式,并加以推广．新方法有别于将有理分式化为部分分式之和的常用方法．     

期权定价Black-scholes公式的一个新推导

文章提出Black scholes公式的一个新推导.在风险中性定价的框架下,通过对正态分布的性质及其矩母函数的熟练运用,可以快速容易地导出Black-scholes公式.并且在此推导过程中,公式中的概率值Φ(d1),Φ(d2)的含义得以明确体现.     

On -analogues of the Euler constant and Lerch's limit formula

We introduce and study a -analogue of the Euler constant via a suitably defined -analogue of the Riemann zeta function. We show, in particular, that the value is irrational. We also present a -analogue of the Hurwitz zeta function and establish an analogue of the limit formula of Lerch in 1894 for the gamma function. This limit formula can be regarded as a natural generalization of the formula of .

     

关于Newton—Leibniz公式的实例分析

通过实例分析,解读Newton-Leibniz公式的应用,旨在澄清关于该公式的一些模糊认识．     

A Remark on Computing the Tame Kernel of Quadratic Imaginary Fields

In this paper, we discuss a method to compute the tame kernel of a number field. Confining ourselves to an imaginary quadratic field, we prove that is bijective when . Received October 25, 1999, Accepted February 5, 2001     

关于虚二次域Tame核计算的一个注记

本文给出了一种计算数域Tame核的方法.应用到虚二次域上,证明了当 Nv>8δD6时,(？)t／:K2S'F／K2SF→k*是双射。     

A Ramanujan Sequence that Refines the Cayley Formula for Trees

A further combinatorial study of Entries 16 and 17 in chapter 3 of Ramanujan's second notebook [1] leads to a refinement of Cayley's formula for counting trees and generalizes the recent results derived by Shor [13], and Dumont and Ramamonjisoa [5]. Our approach also yields a new proof of Clarke's extension of Cayley's formula [4].     

Euler求和公式的一种推广和应用

将只适用于有限区间上具有连续微商的函数的Eu ler求和公式推广到一般的连续函数,并应用此公式推出对于满足L ipsch itz条件的函数普通数值积分的梯形法、矩形法与S im pson法.     

一组三个函数乘积的高阶导数公式及其行列式表示

研究了三个函数乘积的高阶导数,得到了一组相应的导数公式.利用这些公式求该类函数的高阶导数以及进行近似计算,或做函数的近似表示,将起到较好的简化作用.     

从等周不等式谈Green公式的一个应用

Green公式给出了平面图形面积与曲线积分的关系,利用这种关系给出了平面曲线等周不等式的一个简捷证明,并给出了平面图形面积的一个近似计算公式以及两个教学计算实例.     

分布函数展开式中的渐进性

主要讨论了分布函数的泰勒展开式中拉格朗日型余项所确定的"中间点"的渐进性,从而为概率的近似计算提供理论依据.     

A Summation Formula for Estimating the Surface Areas of Ellipsoids

In this paper a summation formula for finding the surface area of general ellipsoids is derived.     

Some inequalities involving π and an application to Hilbert's inequality

Some inequalities involving π are proved. As an application, we give some strengthened Hilbert's inequalities.     

Family of Pearson discrete distributions generated by the univariate hypergeometric function 3F2(α1, α2, α3; γ1, γ2; λ)

In this work we present a study of the Pearson discrete distributions generated by the hypergeometric function ₃F₂(α₁, α₂, α₃;γ₁, γ₂; λ), a univariate extension of the Gaussian hypergeometric function, through a constructive methodology. We start from the polynomial coefficients of the difference equation that lead to such a function as a solution. Immediately after, we obtain the generating probability function and the differential equation that it satisfies, valid for any admissible values of the parameters. We also obtain the differential equations that satisfy the cumulants generating function, moments generating function and characteristic function, From this point on, we obtain a relation in recurrences between the moments about the origin, allowing us to create an equation system for estimating the parameters by the moment method. We also establish a classification of all possible distributions of such type and conclude with a summation theorem that allows us study some distributions belonging to this family. © 1997 by John Wiley & Sons, Ltd.     

A Commuting q-Analogue of the Addition Formula for Disk Polynomials

Starting from the addition formula for q-disk polynomials, which is an identity in noncommuting variables, we establish a basic analogue in commuting variables of the addition and product formula for disk polynomials. These contain, as limiting cases, the addition and product formula for little q-Legendre polynomials. As q tends to 1 the addition and product formula for disk polynomials are recovered. Date received: September 29, 1995. Date revised: May 20, 1996.     

Equations for the Jacobian of a hyperelliptic curve

We give an explicit embedding of the Jacobian of a hyperelliptic curve, , into projective space such that the image is isomorphic to the Jacobian over the splitting field of . The embedding is a modification of the usual embedding by theta functions with half integer characteristics.

     

两类虚二次域类数之间关系的一个注记

就素数d=5,13,29,53,173,293时给出了虚二次数域■(-k)与■(-kd)(k>2,k∈■)的类数之间的关系.