Radius of convergence
Practical estimation of radius in the case of real coefficients

Usually, in scientific applications, only a finite number of coefficients c n {\displaystyle c_{n}} are known. Typically, as n {\displaystyle n} increases, these coefficients settle into a regular behavior determined by the nearest radius-limiting singularity. In this case, two main techniques have been developed, based on the fact that the coefficients of a Taylor series are roughly exponential with ratio 1 / r {\displaystyle 1/r} where r is the radius of convergence.
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