n阶等差数列的隐蔽公差

The Enshrouded Difference of Arithmetic Progression with n Order

等差是等差数列最核心的本质特征。高阶等差数列(或称n阶等差数列)是等差数列 的普遍形式,一阶等差数列是n阶等差数列当n=1时的特例。研究表明,高阶等差数列的差分性 质在经济计量领域有明确的体现。例如,单整序列数据I(n)的差分性质即与n阶等差数列密切相 关。遗憾的是,以往所见关于等差数列的讨论,大多围绕其一阶情况展开。有些常见的关于等差数 列的定义也仅仅适用于一阶条件的假定,不能确切描述等差数列的高阶(二阶及以上)情况。为了 适应经济计量研究与实践的发展,有必要重新研讨关于等差数列术语的定义问题。本文尝试提出 高阶等差数列“隐蔽公差”的概念,同时给出n阶等差数列的形式表达以及n阶等差数列公差与其 相对应一阶等差数列公差的换算关系式D=dnn!,其目的在于放宽约束条件,给出能够涵盖n阶等 差数列情况、具有普适性的术语定义。

A core property of the arithmetic progression is the same difference. An arithmetic progression with n order is the common form. The property has been used in the field on econometrics. For example, the difference property of fractional integration serial data I（n）. The case with n=1 has been pointed by ancient papers about the arithmetic progression, and some definition of arithmetic progression is fit on the assumption that n=1 only, couldn＇t cover the cases when n 〉 1. This paper gives some discussions, defines a term en-difference （i. e. enshrouded difference）, shows a general form and a function of common difference D=d^nn! about the arithmetic progressions with n order.