Approximations for Apery's constant ζ(3) and rational series representations involving ζ(2n)

2016/05/31 by Cezar Lupu, Lupu, Cezar, Derek Orr +1
Mathematics · #41A60 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Number Theory (math.NT) #Primary 41A58 #Secondary 40B99

paper · pdf · doi:10.48550/arxiv.1605.09541

openalex publication_date 2016/05/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this note, using an idea from \citeAmo-Carrillo-Sanchez we derive some new series representations involving ζ(2n) and Euler numbers. Using a well-known series representation for the Clausen function, we also provide some new representations of Apery's constant ζ(3). In particular cases, we recover some well-known series representations of π.

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