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# 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[1]
1 ${\displaystyle \sin x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots }$ Madhava's sine series Isaac Newton (1670) and Wilhelm Leibniz (1676)
2 ${\displaystyle \cos x=1-{\frac {x^{2}}{2!}}+{\frac {x^{4}}{4!}}-{\frac {x^{6}}{6!}}+\cdots }$ Madhava's cosine series Isaac Newton (1670) and Wilhelm Leibniz (1676)
3 ${\displaystyle \operatorname {arctg} x=x-{\frac {x^{3}}{3}}+{\frac {x^{5}}{5}}-{\frac {x^{7}}{7}}+\cdots }$ Madhava's series for arctangent James Gregory (1671) and Wilhelm Leibniz (1676)
4 ${\displaystyle {\frac {\pi }{4}}=1-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+\ldots }$ Madhava's formula for π James Gregory (1671) and Wilhelm Leibniz (1676)

## सन्दर्भ

1. Charles Henry Edwards (1994). The historical development of the calculus. Springer Study Edition Series (3 संस्करण). Springer. पृ॰ 205. आई॰ऍस॰बी॰ऍन॰ 978-0-387-94313-8.