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Unformatted text preview: term carefully, because the general form for the term often does not work well. Analytic functions can even be multiplied, but you must treat the power series as polynomials, so lots of like terms must be combined. It’s a mess. They can even be divided when the denominator isn’t zero, but that’s an even bigger mess. EXAMPLES. (1) ∞ X n =0 x n n ! ! = (2) ∞ X j =0 (1) j x 2 j (2 j )! = (3) For f ( z ) = ∞ X n =0 a n ( zx ) n , ﬁnd f (4) ( x ). (4) Rewrite the power series ∞ X n =2 n ( n1) a n x n2 as a power series whose generic or general term involves x n . THERE IS NO HOMEWORK FOR SECTION 5.1 – BUT PLEASE MAKE SURE YOU REVIEW THAT MATERIAL....
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This note was uploaded on 05/19/2010 for the course M 427K taught by Professor Fonken during the Spring '08 term at University of Texas.
 Spring '08
 Fonken
 Differential Equations, Equations, Power Series

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