Timeline for Does the analytical continuation of $\sum f(n) x^n $ always have a branch cut if $f(z)$ has a pole?
Current License: CC BY-SA 4.0
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| Jan 29, 2023 at 21:42 | vote | accept | Caleb Briggs | ||
| Jan 29, 2023 at 19:23 | comment | added | Barb | Yes, the analytical continuation of a power series of the form ∑f(n)x^n where f(z) has a pole, typically has a branch cut. The presence of a pole in f(z) means that the power series converges only in some region in the complex plane, and outside of this region, the series has to be continued analytically. The cont performed by finding a new representation of function in a different region, often by deforming the contour of integration used in the definition of the series. This process can introduce a branch cut, which is a curve in the complex plane along which the function has a discontinuity | |
| Jan 29, 2023 at 18:42 | history | edited | Caleb Briggs | CC BY-SA 4.0 |
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| Jan 29, 2023 at 8:13 | answer | added | Kostya_I | timeline score: 7 | |
| Jan 29, 2023 at 5:57 | history | asked | Caleb Briggs | CC BY-SA 4.0 |