TL;DR
This paper explores methods for constructing polynomial difference and differential equations from sequences and their generating functions, demonstrating effective D-algebraic operations.
Contribution
It introduces new techniques for deriving D-algebraic equations from sequences and generating functions, enhancing the toolkit for analyzing such mathematical objects.
Findings
Effective methods for constructing polynomial difference equations from sequences
A novel approach to find differential equations for generating functions
Demonstrated success of D-algebraic operations in sequence analysis
Abstract
Given finitely many consecutive terms of an infinite sequence, we discuss the construction of a polynomial difference equation that the sequence may satisfy. We also present a method to seek a candidate polynomial differential equation for its generating function. It appears that these methods often lead to effective D-algebraic operations.
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Taxonomy
TopicsPolynomial and algebraic computation · semigroups and automata theory · Advanced Algebra and Logic