학술논문
Linear recurrence relations for sums of products of two terms.
Document Type
Journal
Author
Mu, Yan-Ping (PRC-TJUT-CS) AMS Author Profile
Source
Subject
05 Combinatorics -- 05A Enumerative combinatorics
05A15Exact enumeration problems, generating functions
33Special functions -- 33F Computational aspects
33F10Symbolic computation
39Difference and functional equations -- 39A Difference equations
39A06Linear equations
68Computer science -- 68W Algorithms
68W30Symbolic computation and algebraic computation
05A15
33
33F10
39
39A06
68
68W30
Language
English
Abstract
Summary: ``For a sum of the form $\sum_k F(n,k)G(n,k)$, we set up two systems of equations involving shifts of $F(n, k)$ and $G(n, k)$. Then we solve the systems by utilizing the recursion of $F(n, k)$ and the method of undetermined coefficients. From the solutions, we derive linear recurrence relations for the sum. With this method, we prove many identities involving Bernoulli numbers and Stirling numbers.''