Functions and Analysis

    

Solving Recurrence Relations Using Generating Functions

Authors: Harry Willow

This paper explores the applications of generating functions in solving various recurrence relations. We present the explicit formulas for recurrence relations of different forms, demonstrating step-by-step transformations and manipulations using generating functions. Several cases are examined, including linear and nonlinear recurrences, factorial-based sequences, and Fibonacci-related expressions. The derivations leverage algebraic techniques and characteristic equations to obtain closed-form solutions. The results highlight the power of generating functions in simplifying complex recurrence relations and deriving explicit formulas efficiently.

Comments: 7 Pages.

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Submission history

[v1] 2025-03-22 08:10:22

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