n 的多项式为系数的幂级数和函数注记  

A Remark for Sum Functions of Power Series with Polynomials of n as Coefficients

作　　者：张奇业[1,2] 王创坤 徐宇鑫 ZHANG Qiye;WANG Chuangkun;XU Yuxin(School of Mathematical Science,Beihang University,Beijing 102206,China;The Key Lab of Mathematics,Information and Behavior of Ministry of Education,Beijing 102206,China;School of Astronautics,Beihang University,Beijing 102206,China;School of Electronic Information and Electrical Engineering,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]北京航空航天大学数学科学学院,北京102206 [2]数学、信息与行为教育部重点实验室,北京102206 [3]北京航空航天大学宇航学院,北京102206 [4]上海交通大学电子信息与电气工程学院,上海200240

出　　处：《大学数学》2024年第1期99-107,共9页College Mathematics

基　　金：北京航空航天大学一流课程项目(42020049);北京航空航天大学教改项目(403735)。

摘　　要：研究了以n的多项式为系数的幂级数的和函数的求解问题,给出了这类幂级数和函数的一种求解方法,并得到了其和函数的通用计算公式,通过实例验证了公式的正确性.文中还得到了两个关于组合数的等式.This paper focuses on the solution to sum functions of power series with polynomials of n as coefficients.A novel method is suggested for computing sum functions of this kind of power series,and general summation formula are provided for them.Finally,some examples are shown to verify the correction of the summation formula.Two formulas for combinatorial numbers are also obtained.

关 键 词：幂级数 多项式系数 和函数 通用形式 数学归纳法 

分 类 号：O13[理学—数学]