Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S1 / 1 / a

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Solution

e^{- 1/ z} = \sum_{n = 0}^{\infty} \frac{( - 1 ) ^{n}}{n !} z^{- n} = 1 - \frac{1}{z} + \frac{1}{2 z ^{2}} - \frac{1}{6 z ^{3}} + \dots, z \neq = 0.

(1)

Its principal part contains infinitely many nonzero negative powers, so zero is an essential singularity. The first three displayed terms are not an asymptotic truncation as

z \to 0

; they are the beginning of the convergent Laurent series in powers of

1/ z

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Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford
Short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford
Physics course of the University of Oxford
Undergraduate course of the University of Oxford
Course of the University of Oxford
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Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S1 / 1 / a

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