General Mathematics

    

A Family of Analytic π-Series via Modulus-q Expansions

Authors: Tajmul Khan

We present a new analytic framework for generating infinite series representations of pi. Using the digamma reflection formula and a modulus-q expansion strategy, we construct families of convergent pi-series. In particular, we derive a novel modulus-5 weighted series (Khan's pi-series), which converges absolutely and exhibits faster convergence than the classical Leibniz series. The approach generalizes naturally to arbitrary moduli q >= 3, yielding entire families of pi-series with adjustable convergence behaviour.

Comments: 13 Pages. (Note by viXra Admin: Please cite listed scientific references)

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[v1] 2026-02-19 20:14:58

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