Discrete Generating Functions

被引：1
|
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.
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页码：1087 / 1093
页数：7
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