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## Homework Statement

**This problem is from Mary L. Boas - Mathematical Methods in the Physical Sciences, Chapter 14, section 3, problem 23.**

**[itex]\oint_C \frac{e^{3z}dz}{(z - ln2)^{4}}[/itex]**

2. Homework Equations

2. Homework Equations

Cauchy's integral formula

## The Attempt at a Solution

**First isolate the singularity:**

**[itex]\oint_C \frac{e^{3z}dz}{(z - ln2)^{4}}[/itex] (This should read something like (e^3z/1^4)/(z-ln2)^4) but I can't seem to do it in latex...)**

**Then let g(z) be:****[itex]g(z) = e^{3z}[/itex]**

**Since there's a fourth power in the singularity, g(z) must be derived three times:**

[itex]g''(z) = 9e^{3z}[/itex]

[itex]g'''(z) = 27e^{3z}[/itex]

**[itex]g'(z) = 3e^{3z}[/itex]**[itex]g''(z) = 9e^{3z}[/itex]

[itex]g'''(z) = 27e^{3z}[/itex]

To solve the integral, we multiply g'''(z) by:

[itex] (2 \pi i)(27e^{(3)(ln2)}) = 432 \pi i[/itex]

But the book states that the answer is [itex]72 \pi i[/itex], which is exactly 6 times less than my answer. Where did I go wrong?

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