Finding The Radius of Convergence
Two cases arise. The first case is theoretical: when you know all the coefficients then you take certain limits and find the precise radius of convergence. The second case is practical: when you construct a power series solution of a difficult problems you typically will only know a finite number of terms in a power series, anywhere from a couple of terms to a hundred terms. In this second case, extrapolating a plot estimates the radius of convergence.
Read more about this topic: Radius Of Convergence
Famous quotes containing the words finding the and/or finding:
“It makes little sense to spend a month teaching decimal fractions to fourth-grade pupils when they can be taught in a week, and better understood and retained, by sixth-grade students. Child-centeredness does not mean lack of rigor or standards; it does mean finding the best match between curricula and children’s developing interests and abilities.”
—David Elkind (20th century)
“Scholars dream of finding small facts pregnant with great progeny.”
—Mason Cooley (b. 1927)