radius of convergence in a sentence

Examples

1. If is equal to its Taylor series for all in the complex plane, it is called diverges at if the distance between and is larger than the radius of convergence.
2. In practical calculations, it is usually required that the sums be analytic within some radius of convergence; typically with a radius of convergence of | x-y |.
3. In practical calculations, it is usually required that the sums be analytic within some radius of convergence; typically with a radius of convergence of | x-y |.
4. Its radius of convergence is at least as large as the minimum of the radii of convergence of p ( x ), q ( x ) and g ( x ).
5. Taylor series are great when they converge quickly, not so great when they converge slowly, and useless outside the radius of convergence where they don't converge at all.
6. Since the moment generating function M _ X ( \ alpha; \ beta; \ cdot ) has a positive radius of convergence, the beta distribution is determined by its moments.
7. The function f ( z ) can have singularities in the complex plane ( branch point singularities, poles or essential singularities ), which limit the radius of convergence of the series.
8. In the case { } _ 2F _ 1, the radius of convergence of the series is 1 and the fraction on the left hand side is a meromorphic function within this circle.
9. The radius of this disc is known as the radius of convergence, and can in principle be determined from the asymptotics of the coefficients " a " " n ".
10. The interesting cases are where " f " is then of radius of convergence equal to 1, and we suppose that the problem as posed has been modified to present this situation.