Year: 2026
Type: preprint
Abstract: By utilizing two known hypergeometric summation identities, we extend two \mbox{well-known} Ramanujan series for $1/π$ by making each of them a member of an infinite family of series. We also find the corresponding families involving harmonic numbers and odd harmonic numbers. To further illustrate our method we derive families of \mbox{Ramanujan-like} series for $1/π$ associated with a hypergeometric series derived by Lavoie, two hypergeometric series from Bailey's book and a recent hypergeometric series found by Campbell. Thus, by leveraging known hypergeometric summation identities, our approach bypasses the more tedious, traditional limits or complex Fourier-Legendre expansions; offering a cleaner, unified template for generating Ramanujan-like series for $1/π$.
Source: arXiv (Cornell University)
Author: Adegoke, Kunle
Institution: Obafemi Awolowo University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212167771