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:
“A child is born with the potential ability to learn Chinese or Swahili, play a kazoo, climb a tree, make a strudel or a birdhouse, take pleasure in finding the coordinates of a star. Genetic inheritance determines a child’s abilities and weaknesses. But those who raise a child call forth from that matrix the traits and talents they consider important.”
—Emilie Buchwald (20th century)
“There comes a point in many people’s lives when they can no longer play the role they have chosen for themselves. When that happens, we are like actors finding that someone has changed the play.”
—Brian Moore (b. 1921)