New series representations of π, π3 and π5 in terms of Euler numbers and π2, π4 and π6 in terms of Bernoulli numbers

2017/10/10 by Himanshu Gupta, Gupta, H C
Mathematics · #11B50 #11B68 #Advanced Mathematical Identities #FOS: Mathematics #General Mathematics (math.GM) #Mathematical Inequalities and Applications #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1710.04083

openalex publication_date 2017/10/10 · openalex created_date 2017/10/20 · openalex updated_date 2026/07/28

Abstract

New series representations for odd powers of π i.e. π, π3 and π5 in terms of Euler numbers and even powers of π i.e. π2, π4 and π6 in terms of Bernoulli numbers have been obtained empirically.

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