homework20111028

homework20111028 - a) 7 z 1 4 z 3 b) e 3 z 2 c) z cos( z 2...

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Math 417, Fall 2011 Exercise Set #6 Turn in: October 28 1. Evaluate ° C 2 z +1 z 4 2 z 2 +1 dz ,whe re C is the circle | z | =10w i ththepo s i t iv e orientation. 2. Show that if ± n =1 z n = S ,then ± n =1 z n = S . 3. What is the radius of convergence of the Taylor Series for f ( z )= 1 z 2 3 z +2 about z = 0? About z =3 i ? 4. Find the radius of convergence for the following power series: a) ± n =1 nz n b) ± n =1 z n n c) ± n =1 z n n ! d) ± n =1
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Unformatted text preview: a) 7 z 1 4 z 3 b) e 3 z 2 c) z cos( z 2 ) d) z cosh( z 2 ) 1 2 . 6. Find elementary expressions for the following power series a) n =1 z 3 n +1 b) n =1 n ( n 1) z n c) n =1 z 2 n n ! 7. Let z = re i where 0 < r < 1. Show that a) n =1 r n cos( n ) = r cos( ) r 2 1 2 r cos( ) + r 2 b) n =1 r n sin( n ) = r sin( ) 1 2 r cos( ) + r 2...
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This note was uploaded on 02/27/2012 for the course MATH 417 taught by Professor Staff during the Fall '11 term at SUNY Albany.

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homework20111028 - a) 7 z 1 4 z 3 b) e 3 z 2 c) z cos( z 2...

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