2023/03/20 by Neha Elizabeth Thomas, Thomas, Neha Elizabeth, K Vishnu Namboothiri +1
Computer Science · Mathematics · #05A18 #11B37 #11B75 #11L03 #Advanced Algebra and Logic #Advanced Mathematical Identities #Computability, Logic, AI Algorithms #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2303.10853
openalex publication_date 2023/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using combinatorial techniques, we derive a recurrence identity that expresses an exponential power sum with negative powers in terms of another exponential power sum with positive powers. Consequently, we derive a formula for the power sum of the first k natural numbers when the power is odd, which when used in combination with Faulhaber's formula for computing power sums helps us to retrieve the Bernoulli numbers in certain cases.