摘要
在1884年,当斯蒂尔杰斯研究高斯关于某种定积分的近似计算公式时,惊讶地发现连分数与定积分之间的某种奇妙关系.他花费10年时间终于探明这一事实的一般性:他把力学中矩问题与源于积分的“自然”连分数联系起来,建立了一种新的积分———Stieltjes-积分(以下简称为S-积分),完成了对R-积分的第一次推广.几乎同时,匈牙利数学家柯尼克在研究R-积分第二中值定理时,在不经意之中推广了S-积分.又过了大约10年,匈牙利数学家里斯利用S-积分提供了有限区间上的连续函数空间中的线性泛函的一般表示形式.在20世纪第2个10年中,许多数学家都在推广并应用这种积分.人们发现,S-积分与许多数学分支都有着非常广泛的联系,对许多理论和实际问题的解决都是十分有效的.这里作者主要讨论S-积分的产生、发展和应用,努力遵循理论发展与应用需要这两条线索,尝试从数学思想史的角度来展开讨论.
In 1884, Stieljes discovered surprisingly the wonderful relation of continued fraction and definite integral, when he studied Gauss＇approximate computing formula in certain definite integral. He spent 10 years to finally dig out the universality in this fact： he related the problem of moment in physics with the ＂natural＂ continued fraction originating from integral, thereby he discovered a new integral m Stieltjes integral, which is the first generalization of Riemann integral. At the same time, Hungary mathematician Konig generalized Stieltjes integral accidentally in the course of researching the second mean value theorem in Riemann integral. About 10 years later, Hungary mathematician Riesz brought forward the general expression for linear functional in finite interval. In the second 10 year of 20th century, many mathematicians extended and applied this integral. People found that Stieltjes integral had a wide relationship with many embranchments of mathematics, and it also had an effect on solving academic and applied problems. This thesis mainly focuses on discussing the origin , development and application of Stieltjes integral, the author tries to discuss this integral through the thinking history of mathematics by the thread of theory development and application need,
出处
《广西民族学院学报（自然科学版）》
CAS
2006年第1期37-42,共6页
Journal of Guangxi University For Nationalities(Natural Science Edition)
关键词
矩问题
连分式
S-积分
线性泛函
moment problem
continued fraction
Stieltjes integral
linear functional
