2024/11/24 by Ern, Thang Pang, Wangsa, Devandhira Wijaya
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2411.15803
In 1914, Ramanujan presented a collection of 17 elegant and rapidly converging formulae for π. Among these, one of the most celebrated is the following series: \frac1π=(2√(2))/(9801)∑n=0∞(26390n+1103)/((n!)4)⋅ \frac(4n)!3964n In this paper, we give a full proof of this classic formula using hypergeometric series and a special type of lattice sums due to Zucker and Robertson. We will also use some results by Dirichlet and Edwards in algebraic number theory.