Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a Madhava series is any one of the series in a collection of infinite series expressions all of which are believed to have been discovered by Sangamagrama Madhava the founder of the Kerala school of astronomy and mathematics. These expressions are the infinite power series expansions of the trigonometric sine, cosine and arctangent functions, and the special case of the power series expansion of the arctangent function yielding a formula for computing . The power series expansions of sine and cosine functions are respectively called Madhava's sine series and Madhava's cosine series. The power series expansion of the arctangent function is sometimes called Madhava–Gregory series or Gregory–Madhava series. These power series are also collectively called Taylor–Madhava series. The formula for is referred to as Madhava–Newton series or Madhava–Leibnitz series or Leibniz formula for pi or Leibnitz–Gregory–Madhava series. These further names for the various series are reflective of the names of the western discoverers or popularizers of the respective series.

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