What Historians of Mathematics Recognise
From Mādhava's Sphuṭacandrāpti — the True Moon and the Infinite Series, taught by Acharya T Krishnatrey. This lesson is free to read.
<pre data-block="research">The Kerala school founded by Mādhava is recognised as having obtained, centuries before Europe: the infinite series for π (the "Gregory–Leibniz" series), the power series for sine and cosine (the "Newton" series), an end-correction accelerating the π series, and π to eleven decimal places. Jyeṣṭhadeva's Yuktibhāṣā goes further and supplies DEMONSTRATIONS of these results. Mādhava's own treatises on the series are lost; the results are known because Nīlakaṇṭha, Śaṅkara Vāriyar and Jyeṣṭhadeva quote and credit him by name. His Sphuṭacandrāpti, by contrast, survives in a manuscript in his own words.</pre>