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Isolated Singularities and Series Expansions

Part 1: Taylor Series Expansions

  1. Enter the series command in your worksheet. Experiment with generating a series with more terms.

  2. How does the series expansion for sinh(z) at z = 0 compare with the corresponding expansion for sin(z)?

  3. Repeat the experiment in Step 2 for cosh(z) and cos(z).

  4. Find the coefficient of (z - i)5 in the expansion of cosh(z) about z = i.

  5. Find the coefficient of (z + 1)8 in the expansion of sinh(z) about z = -1.

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