A Short Proof of Knuth's Old Sum

2024/11/22 by Kunle Adegoke, Adegoke, Kunle
Computer Science · #05A10 #05A19 #Computability, Logic, AI Algorithms #FOS: Mathematics #General Mathematics (math.GM) #Parallel Computing and Optimization Techniques #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2412.00040

openalex publication_date 2024/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a short proof of the well-known Knuth's old sum and provide some generalizations. Our approach utilizes the binomial theorem and integration formulas derived using the Beta function. Several new polynomial identities and combinatorial identities are derived.

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