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-	{{Infobox Settlement	+	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 (c. 1350 – c. 1425) 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 π. 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[1][2] or Gregory–Madhava series. These power series are also collectively called Taylor–Madhava series.[3] The formula for π is referred to as Madhava–Newton series or Madhava–Leibnitz series or Leibniz formula for pi or Leibnitz–Gregory–Madhava series.[4] These further names for the various series are reflective of the names of the western discoverers or popularizers of the respective series.
-	| name = Jaworowo-Kolonia	+
-	| settlement_type = Village	+
-	| total_type =  	+
-	| image_skyline =	+
-	| image_caption =	+
-	| image_flag =	+
-	| image_shield =	+
-	| image_map =	+
-	| subdivision_type = [[Countries of the world|Country]]	+
-	| subdivision_name = {{flag icon|Poland}} [[Poland]]	+
-	| subdivision_type1 = [[Voivodeships of Poland|Voivodeship]]	+
-	| subdivision_name1 = [[Masovian Voivodeship|Masovian]]	+
-	| subdivision_type2 = [[Powiat|County]]	+
-	| subdivision_name2 = [[Sierpc County|Sierpc]]	+
-	| subdivision_type3 = [[Gmina]]	+
-	| subdivision_name3 = [[Gmina Zawidz|Zawidz]]	+
-	| elevation_m =	+
-	| population_total =	+
-	| website = }}	+
-	'''Jaworowo-Kolonia''' {{IPAc-pl|j|a|w|o|'|r|o|w|o|-|k|o|'|l|o|ń|a}} is a [[village]] in the administrative district of [[Gmina Zawidz]], within [[Sierpc County]], [[Masovian Voivodeship]], in east-central Poland.<ref name="TERYT">{{cite web |url=http://www.stat.gov.pl/broker/access/prefile/listPreFiles.jspa |title=Central Statistical Office (GUS) - TERYT (National Register of Territorial Land Apportionment Journal) |date=2008-06-01 |language=Polish}}</ref>	+
-	==References==	+	No surviving works of Madhava contain explicit statements regarding the expressions which are now referred to as Madhava series. However, in the writing of later members of the Kerala school of astronomy and mathematics like Nilakantha Somayaji and Jyeshthadeva one can find unambiguous attributions of these series to Madhava. It is also in the works of these later astronomers and mathematicians one can trace the Indian proofs of these series expansions. These proofs provide enough indications about the approach Madhava had adopted to arrive at his series expansions.
-	{{reflist}}	+
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-	<br>	+
-	{{Gmina Zawidz}}	+
-		+
-	{{coord missing|Masovian Voivodeship}}	+
-		+
-	[[Category:Villages in Sierpc County|Jaworowo-Kolonia]]	+
-	{{Sierpc-geo-stub}}	+
-		+
-	[[pl:Jaworowo-Kolonia]]	+

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Revision as of 19:28, 24 June 2010

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 (c. 1350 – c. 1425) 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 π. 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[1][2] or Gregory–Madhava series. These power series are also collectively called Taylor–Madhava series.[3] The formula for π is referred to as Madhava–Newton series or Madhava–Leibnitz series or Leibniz formula for pi or Leibnitz–Gregory–Madhava series.[4] These further names for the various series are reflective of the names of the western discoverers or popularizers of the respective series.

No surviving works of Madhava contain explicit statements regarding the expressions which are now referred to as Madhava series. However, in the writing of later members of the Kerala school of astronomy and mathematics like Nilakantha Somayaji and Jyeshthadeva one can find unambiguous attributions of these series to Madhava. It is also in the works of these later astronomers and mathematicians one can trace the Indian proofs of these series expansions. These proofs provide enough indications about the approach Madhava had adopted to arrive at his series expansions.