Discrete Generating Functions

被引：2

作者：

Akhtamova, S. S. ^{[1
]}

Alekseev, V. S. ^{[2
]}

Lyapin, A. P. ^{[2
]}

机构：

[1] Siberian Fed Univ, Lesosibirskij Pedag Inst Branch, Lesosibirsk 662544, Russia

[2] Siberian Fed Univ, Sch Mathemat & Comp Sci, Krasnoyarsk 660041, Russia

来源：

MATHEMATICAL NOTES | 2023年 / 114卷 / 5-6期

关键词：

generating function; D-finiteness; p-recursiveness; generating series; forward difference operator;

D O I：

10.1134/S000143462311041X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The notion of a discrete generating function is defined. The definition uses the falling factorial instead of a power function. A functional equation for the discrete generating function of a solution to a linear difference equation with constant coefficients is found. For the discrete generating function of a solution to a linear difference equation with polynomial coefficients, the notion of D-finiteness is introduced and an analog of Stanley's theorem is proved; namely, a condition for the D-finiteness of the discrete generating function of a solution to such an equation is obtained.

引用

页码：1087 / 1093

页数：7