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SERINGAPATAM, or SRIRANGAPATANA

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Originally appearing in Volume V24, Page 672 of the 1911 Encyclopedia Britannica.
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See also:

SERINGAPATAM, or SRIRANGAPATANA , a See also:town of See also:India, formerly See also:capital of the See also:state of See also:Mysore, situated on an See also:island of the same name in the See also:Cauvery See also:river. Pop. (1901) 8584. The town is chiefly noted for its fortress, which figured prominently in See also:Indian See also:history at the See also:close of the 18th See also:century. This formidable stronghold of Tippoo See also:Sultan twice sustained a See also:siege from the See also:British, and was finally stormed in 1799. After its See also:capture the island was ceded to the British, but restored to Mysore in 1881. The island of Seringapatam is about 3 M. in length from See also:east to See also:west and i in breadth, and yields valuable crops of See also:rice and See also:sugar-See also:cane. The fort occupies the western See also:side, immediately overhanging the river. Seringapatam is said to have been founded in 1454 by a descendant of one of the See also:local See also:officers appointed by Ramanuja, the Vishnuite apostle, who named it the See also:city of Sri Ranga or See also:Vishnu. At the eastern or See also:lower end of the island is the Lal Bagh or " red See also:garden," containing the See also:mausoleum built by Tippoo Sultan for his See also:father Hyder See also:Ali, in which Tippoo himself also lies. The See also:series is then said to converge uniformly throughout this region. If, as z approaches the value z1, n increases as lz diminishes and becomes indefinitely See also:great as I z—zi I becomes indefinitely small the series is said to be non-uniformly convergent at the point zi.

A See also:

function represented by a series is continuous throughout any region in which the series is uniformly convergent; there cannot be discontinuity with See also:uniform convergence; on the other See also:hand there may be continuity and non-uniform convergence. If ul (z) +uz(z) +... is uniformly convergent we shall have fS(z)dz=fui(z)dz+fuz(z)dz+... along any path in the region of uniform convergence ;'and we shall also have- S(z)=dZ 1(z)+dzuz(z)+...if the series dzui(s)+dzuz(z) + . . . is uniformly convergent. Uniform convergence is essentially different from See also:absolute convergence; neither implies the other (see FUNCTION). 18. A series of the See also:form ao+alz+azz2+ . . ., in which ao, a1, az, .. . are See also:independent of z, is called a See also:power series. In the See also:case of a power series there is a quantity R such that the series converges if 1z 1< R, and diverges if z 1>R. A circle de-scribed with the origin as centre and See also:radius R is called the circle of convergence. s A power series may or may not converge on the circle of convergence. The circle of convergence may be of a See also:infinite radius as in the case of the series for See also:sin z, viz.

End of Article: SERINGAPATAM, or SRIRANGAPATANA

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