PP 12.9 - Representations of Functions as Power Series...

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Unformatted text preview: Representations of Functions as Power Series Comments 1 if converges it that and series geometric a as viewed be can series that the know We < = x x n n =-- = 1 1 1 that know also We n n r a ar 1 , 1 1 1 1 <- = = = =- x x x x n m m n function. for the tion representa series a have then we , 1 1 ) ( if So, x x f- = Of course, this representation is good only for | x | < 1. Example e. convergenc of radius its Determine . 2 3 ) ( for tion representa series power a Find x x f- = 1 2 , 2 2 3 1 1 2 3 2 3 2 < = - =- = x x x n n x 2 , 2 3 2 3 1 < =- = + x x x n n n So, R = 2. Example . 2 3 ) ( for tion representa series power a Find 2 x x x f- = 2 , 2 3 2 3 1 < =- = + x x x n n n 2 , 2 3 2 3 1 2 2 < =- = + + x x x x n n n Differentiation and Integration of Power Series . radius with e convergenc of interval has ) ( Assume- = R a x c n n n . interval on the ) ( Assume =- = n n n a x c f(x) . ) , ( on able differenti is Then R a R a f(x) +- )...
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This note was uploaded on 01/21/2011 for the course PHYS 4A 60865 taught by Professor L. oldewurtel during the Fall '09 term at Irvine Valley College.

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PP 12.9 - Representations of Functions as Power Series...

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