New Generalizations of Two Ramanujan Series for $1/π$

Kunle Adegoke

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arXiv · 2609.09209

New Generalizations of Two Ramanujan Series for $1/π$

Kunle Adegoke

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Abstract

By utilizing two hypergeometric summation identities we extend two 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 a family of Ramanujan-like series associated with a hypergeometric series derived by Lavoie.

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Kunle Adegoke. 2026-09-16. New Generalizations of Two Ramanujan Series for $1/π$. https://arxiv.org/abs/2609.09209

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