Gave infinite series for sine, cosine and the arctangent, with the estimates of their error — results transmitted and proved in the Yuktibhasha of the school he founded.
Aryabhatiya
Fourteenth to fifteenth century CE · range · probable
Dated through his pupils and the commentaries of the Kerala school
Sangamagrama — today Kerala · Kerala (probable)
Mathematics and mathematical sciences — Ganita and Chandah-shastra. Algebra and indeterminate equations, combinatorics, infinite series for trigonometric functions, iterative approximation.
Evidence: probable · no modern scholarly reference recorded yet.