<Dl> <Dd> π 4 = 3 4 + 1 3 3 − 3 − 1 5 3 − 5 + 1 7 3 − 7 − ⋯ (\ displaystyle (\ frac (\ pi) (4)) = (\ frac (3) (4)) + (\ frac (1) (3 ^ (3) - 3)) - (\ frac (1) (5 ^ (3) - 5)) + (\ frac (1) (7 ^ (3) - 7)) - \ cdots) </Dd> </Dl> <Dd> π 4 = 3 4 + 1 3 3 − 3 − 1 5 3 − 5 + 1 7 3 − 7 − ⋯ (\ displaystyle (\ frac (\ pi) (4)) = (\ frac (3) (4)) + (\ frac (1) (3 ^ (3) - 3)) - (\ frac (1) (5 ^ (3) - 5)) + (\ frac (1) (7 ^ (3) - 7)) - \ cdots) </Dd> <Ul> <Li> Using the improved series to derive a rational expression, 104348 / 33215 for π correct up to nine decimal places, i.e. 3.141592653 . </Li> <Li> Use of an intuitive notion of limit to compute these results . </Li> <Li> A semi-rigorous (see remark on limits above) method of differentiation of some trigonometric functions . However, they did not formulate the notion of a function, or have knowledge of the exponential or logarithmic functions . </Li> </Ul> <Li> Using the improved series to derive a rational expression, 104348 / 33215 for π correct up to nine decimal places, i.e. 3.141592653 . </Li>

Indian scholars contributed to mathematics by developing the decimal system and the concept of zero