Content deleted Content added
converting raw html to latex |
→Calculation: Added a tip-off that the condition in the last sentence would be coming |
||
Line 16:
* <math>\Gamma_k</math> lies inside <math>\Gamma_{k+1}</math> for all <math>k</math>
* <math>\lim_{k\rightarrow \infty} d(\Gamma_k) = \infty</math>, where <math>d(\Gamma_k)</math> gives the distance from the curve to the origin
* one more condition of compatibility with the poles <math>\lambda_k</math>, described at the end of this section
Suppose also that there exists an integer <math>p</math> such that
Line 48 ⟶ 49:
:<math>\sum_{j=0}^p c_{j,k}z^j = [\operatorname{Res}_{z=\lambda_k} f(z)] \sum_{j=0}^p \frac{1}{\lambda_k^{j+1}} z^j</math>
* To avoid issues with convergence, the poles should be ordered so that if <math>\lambda_k</math> is inside <math>\Gamma_n</math>, then <math>\lambda_j</math> is also inside <math>\Gamma_n</math> for all <math>j < k</math>.
==Example==
| |||