What is the coefficient of \(z^{-3}\) in the Laurent series of \(e^{1/z}\) on \(0<|z|\)?

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Review the concept: Laurent series

The Laurent series of a function \(f\) holomorphic on an annulus \(r<|z-z_0|<R\) is its expansion in integer powers, positive and negative, of \(z-z_0\), with coefficients \(a_n\).

More practice problems: laurent series

• ZW-LAURENT-SERIES-002 Find the coefficient of z^-1 in the Laurent expansion of z^2sin (1/z) on 0<|z|.
• ZW-LAURENT-SERIES-003 On 0<|z|<1, how many terms with a negative power does the Laurent series of 1z^2(1-z) have?
• ZW-LAURENT-SERIES-004 What is the Laurent series of 1z-1 on the region |z|>1?
• ZW-LAURENT-SERIES-005 Compute oint_|z|=1e^3/z dz, with the circle traversed once counterclockwise.
• ZW-LAURENT-SERIES-006 If f is holomorphic on the whole disc |z-z_0|<R, what does its Laurent series on 0<|z-z_0|<R look l…
• ZW-LAURENT-SERIES-007 Let f(z)=1(z-1)(z-2). On the annulus 1<|z|<2, what is the coefficient a_0?
• ZW-LAURENT-SERIES-008 Which integral gives the coefficient a_-2 of the Laurent series of f about z_0 (over a circle insid…
• ZW-LAURENT-SERIES-009 Find the coefficient of (z-1)^-1 in the Laurent series of (e^z)/((z-1)^2) on 0<|z-1|.

ZW-LAURENT-SERIES-002 →