माधव श्रेणी
गणित में संगमग्राम के माधव ने कई श्रेणीयाँ दीं जिन्हें लैब्नीज श्रेणी भी कहते हैं।
| No. | Series | Name | Western discoverers of the series and approximate dates of discovery[१] |
|---|---|---|---|
| 1 | <math>\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots </math> | Madhava's sine series | Isaac Newton (1670) and Wilhelm Leibniz (1676) |
| 2 | <math>\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots </math> | Madhava's cosine series | Isaac Newton (1670) and Wilhelm Leibniz (1676) |
| 3 | <math>\operatorname{arctg} x = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \cdots </math> | Madhava's series for arctangent | James Gregory (1671) and Wilhelm Leibniz (1676) |
| 4 | <math>\frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \ldots </math> | Madhava's formula for साँचा:Pi | James Gregory (1671) and Wilhelm Leibniz (1676) |