关于含有Stirling公式的几个双边不等式的注记

关注三个都含有Stirling公式形式简短易用的双边不等式.对其中之一得出了新的下界(左边)不等式.又根据双边逼近的观点,验证了改进后的不等式在逼近精度上优于Robbins的双边不等式.     

广义Stirling数偶的理论及应用

The object of this expository paper is to sum up several results concerning generalized Stirling number (GSN) pairs investigated earlier by the author. Also expounded in some detail are two kinds of extended GSN pairs with applications (illustrative examples).     

Generalized Mbius Inversion with Applications to Integral Equations and Interpolation Process

The object of this expository paper is to establish a kind of generalized M(?)bius-Rota inversion formula by the aid of non-standard analysis. Certain constructive applications to Volterra type integral equations and toequidistant smooth interpolation process are expounded in some detail. Moreover, some of our earlier results (cf. [1], [2], [4]) are refined and improved.     

略论科学计算在理论研究中的作用

本文略述“科学计算”的内容、方法和意义,并通过两个特别引人注目的事例的介绍,着重阐述科学计算对理论研究的重大作用.     

关于一类复合幂级数展开式的收敛性定理

本文研究了一类复合型幂级数展开式,证明了一个收敛性定理并举例说明其应用.在注记中指出了可进一步研究的问题.     

Hilbert重级数定理的一个改进

The object of this note is to prove the followingTheorem Let{a_n}and{b_n}be sequences of real numbers such that0<∑∑a_n~2<+∞and0<∑b_n~2<+∞.Then we have the inequalitysum from m=1 to∞sum from n=1 to∞a_mb_n/m+n<{sum from n=1 to∞(π-θ/n~(1/2)a_n~2}~1/2{sum from n=1 to∞(π-θ/n~(1/2)b_n~2}~1/2 (1)whereθ=3/2~(1/2)-1=1.121320343.     

由Lagrange展开产生的一对公式

Let Γ denote the ring of formal power series over the complex field C. Let φ∈Γ with φ(0)=0 and φ′(0)=0 So that it has a compositional inverse ψ with ψ(φ(t))=φ(ψ(t))=1. Then for every f∈Γ and α∈C With α≠0 we have Lagrange′s formal expansion