A NOTE ON A HYPERGEOMETRIC SERIES BASED SOLUTION TO THE BASEL PROBLEM

• 발행기관: 충청수학회
• 저자명: Arjun Kumar Rathie Dongkyu Lim
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 38, No. 1, 1~8쪽, 전체 8쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2025.02.28

국문 초록

In a very recent paper, Campbell [A Wilf-Zeilbeger based solution to the Basel problem with applications, Discrete Math. Lett. 10 (2022), 21-27], after re-writing the Basel series into a 3F2(1) hypergeometric series, pointed out that “it is not obvious as to have classically known hypergeometric identities for 3F2(1)-series with free parameters such as those of Dixon’s summation identity, Whipple’s summation identity orWatson’s summation identity could be used to determine a full proof for the closed form 3F2(1)-Basel series”. Thus the aim of this note is to provide the solution of the 3F2(1)-Basel series via the above-mentioned three summation identities.

목차

1. Introduction

2. Derivation of Basel series

References

키워드

Basel problem WZ theory hypergeometric series summations Dixon identity Whipple identity Watson identity Riemann zeta function