Abstract
The subject of complex analysis is an extremely rich and powerful area of mathematics. We have already seen some of this richness and power in the previous chapter. This chapter concludes our discussion of complex analysis by introducing some other topics with varying degrees of importance.
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Notes
- 1.
This is not a restrictive assumption because we can always move our coordinate system so that the origin avoids all poles.
- 2.
One can “prove” this by factoring the simple zeros one by one, writing g(z)=(z−z 1)f 1(z) and noting that g(z 2)=0, with \(z_{2}\not=z_{1}\), implies that f 1(z)=(z−z 2)f 2(z), etc.
- 3.
Provided that S is not discrete (countable). (See [Lang 85, p. 91].)
- 4.
The angle θ 1 is still ambiguous by π, because n can be 1 or 3. However, by a suitable sign convention described below, we can remove this ambiguity.
References
Hildebrand, F.: Statistical Mechanics. Dover, New York (1987)
Lang, S.: Complex Analysis, 2nd edn. Springer, Berlin (1985)
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Hassani, S. (2013). Advanced Topics. In: Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-01195-0_12
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DOI: https://doi.org/10.1007/978-3-319-01195-0_12
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