Quiz5 - ∴ =-⋅⋅⋅ 2 3 1 1 1 1 1 1 2 1 1 2 2 n n n n n...

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Quiz 5 Find the Laurent expansion for ( 29 ( 29 ( 29 1 1 2 f z z z = - - valid for 1 2 z < < . (Hint: Use partial fractions to write ( 29 f z in the form ( 29 ( 29 ( 29 1 2 A B f z z z = + - - and expand the first one for 1 z and the second for 2 z < .) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 1 0, 2 1 1 2 1 2 1, 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 2 1 2 4 8 A B f z A B A B z z z z A B f z z z z for z z z z z z z z z z for z z z z z f z = = + + = - - = - - - - = - = = - + - -   - = - = - = - + + +⋅⋅⋅   -   - -   = - = - + + +⋅⋅⋅ <  
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Unformatted text preview: - - ∴ = ----⋅⋅⋅ 2 3 1 1 1 1 1 1 2 1 1 2 2 n n n n n for z z z z z z for z ∞ ∞-+ = = + ----⋅⋅⋅ < < =-+-< < ∑ ∑ (Note: Putting the solution in the form with summation signs is not required. The form with ellipses is sufficient.)...
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